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Simplifying x(x + 3) = 117 Reorder the terms: x(3 + x) = 117 (3 * x + x * x) = 117 (3x + x2) = 117 Solving 3x + x2 = 117 Solving for variable 'x'. Reorder the terms: -117 + 3x + x2 = 117 + -117 Combine like terms: 117 + -117 = 0 -117 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '117' to each side of the equation. -117 + 3x + 117 + x2 = 0 + 117 Reorder the terms: -117 + 117 + 3x + x2 = 0 + 117 Combine like terms: -117 + 117 = 0 0 + 3x + x2 = 0 + 117 3x + x2 = 0 + 117 Combine like terms: 0 + 117 = 117 3x + x2 = 117 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 + x2 = 117 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 117 + 2.25 Combine like terms: 117 + 2.25 = 119.25 2.25 + 3x + x2 = 119.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 119.25 Calculate the square root of the right side: 10.920164834 Break this problem into two subproblems by setting (x + 1.5) equal to 10.920164834 and -10.920164834.Subproblem 1
x + 1.5 = 10.920164834 Simplifying x + 1.5 = 10.920164834 Reorder the terms: 1.5 + x = 10.920164834 Solving 1.5 + x = 10.920164834 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 = 10.920164834 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 10.920164834 + -1.5 x = 10.920164834 + -1.5 Combine like terms: 10.920164834 + -1.5 = 9.420164834 x = 9.420164834 Simplifying x = 9.420164834Subproblem 2
x + 1.5 = -10.920164834 Simplifying x + 1.5 = -10.920164834 Reorder the terms: 1.5 + x = -10.920164834 Solving 1.5 + x = -10.920164834 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 = -10.920164834 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -10.920164834 + -1.5 x = -10.920164834 + -1.5 Combine like terms: -10.920164834 + -1.5 = -12.420164834 x = -12.420164834 Simplifying x = -12.420164834Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.420164834, -12.420164834}
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