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Simplifying x2 + 15x = 176 Reorder the terms: 15x + x2 = 176 Solving 15x + x2 = 176 Solving for variable 'x'. Reorder the terms: -176 + 15x + x2 = 176 + -176 Combine like terms: 176 + -176 = 0 -176 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '176' to each side of the equation. -176 + 15x + 176 + x2 = 0 + 176 Reorder the terms: -176 + 176 + 15x + x2 = 0 + 176 Combine like terms: -176 + 176 = 0 0 + 15x + x2 = 0 + 176 15x + x2 = 0 + 176 Combine like terms: 0 + 176 = 176 15x + x2 = 176 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 176 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 176 + 56.25 Combine like terms: 176 + 56.25 = 232.25 56.25 + 15x + x2 = 232.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 232.25 Calculate the square root of the right side: 15.239750654 Break this problem into two subproblems by setting (x + 7.5) equal to 15.239750654 and -15.239750654.Subproblem 1
x + 7.5 = 15.239750654 Simplifying x + 7.5 = 15.239750654 Reorder the terms: 7.5 + x = 15.239750654 Solving 7.5 + x = 15.239750654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 15.239750654 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 15.239750654 + -7.5 x = 15.239750654 + -7.5 Combine like terms: 15.239750654 + -7.5 = 7.739750654 x = 7.739750654 Simplifying x = 7.739750654Subproblem 2
x + 7.5 = -15.239750654 Simplifying x + 7.5 = -15.239750654 Reorder the terms: 7.5 + x = -15.239750654 Solving 7.5 + x = -15.239750654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -15.239750654 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -15.239750654 + -7.5 x = -15.239750654 + -7.5 Combine like terms: -15.239750654 + -7.5 = -22.739750654 x = -22.739750654 Simplifying x = -22.739750654Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.739750654, -22.739750654}
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