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Simplifying 21 + (x + 3) * x = 180 Reorder the terms: 21 + (3 + x) * x = 180 Reorder the terms for easier multiplication: 21 + x(3 + x) = 180 21 + (3 * x + x * x) = 180 21 + (3x + x^{2}) = 180 Solving 21 + 3x + x^{2}= 180 Solving for variable 'x'. Reorder the terms: 21 + -180 + 3x + x^{2}= 180 + -180 Combine like terms: 21 + -180 = -159 -159 + 3x + x^{2}= 180 + -180 Combine like terms: 180 + -180 = 0 -159 + 3x + x^{2}= 0 Begin completing the square. Move the constant term to the right: Add '159' to each side of the equation. -159 + 3x + 159 + x^{2}= 0 + 159 Reorder the terms: -159 + 159 + 3x + x^{2}= 0 + 159 Combine like terms: -159 + 159 = 0 0 + 3x + x^{2}= 0 + 159 3x + x^{2}= 0 + 159 Combine like terms: 0 + 159 = 159 3x + x^{2}= 159 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x^{2}= 159 + 2.25 Reorder the terms: 2.25 + 3x + x^{2}= 159 + 2.25 Combine like terms: 159 + 2.25 = 161.25 2.25 + 3x + x^{2}= 161.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 161.25 Calculate the square root of the right side: 12.698425099 Break this problem into two subproblems by setting (x + 1.5) equal to 12.698425099 and -12.698425099.## Subproblem 1

x + 1.5 = 12.698425099 Simplifying x + 1.5 = 12.698425099 Reorder the terms: 1.5 + x = 12.698425099 Solving 1.5 + x = 12.698425099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 12.698425099 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 12.698425099 + -1.5 x = 12.698425099 + -1.5 Combine like terms: 12.698425099 + -1.5 = 11.198425099 x = 11.198425099 Simplifying x = 11.198425099## Subproblem 2

x + 1.5 = -12.698425099 Simplifying x + 1.5 = -12.698425099 Reorder the terms: 1.5 + x = -12.698425099 Solving 1.5 + x = -12.698425099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -12.698425099 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -12.698425099 + -1.5 x = -12.698425099 + -1.5 Combine like terms: -12.698425099 + -1.5 = -14.198425099 x = -14.198425099 Simplifying x = -14.198425099## Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.198425099, -14.198425099}

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