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Simplifying -1x2 + 15x + 52 = 0 Reorder the terms: 52 + 15x + -1x2 = 0 Solving 52 + 15x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -52 + -15x + x2 = 0 Move the constant term to the right: Add '52' to each side of the equation. -52 + -15x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + -15x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -15x + x2 = 0 + 52 -15x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 -15x + x2 = 52 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 = 52 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 52 + 56.25 Combine like terms: 52 + 56.25 = 108.25 56.25 + -15x + x2 = 108.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 108.25 Calculate the square root of the right side: 10.404326023 Break this problem into two subproblems by setting (x + -7.5) equal to 10.404326023 and -10.404326023.Subproblem 1
x + -7.5 = 10.404326023 Simplifying x + -7.5 = 10.404326023 Reorder the terms: -7.5 + x = 10.404326023 Solving -7.5 + x = 10.404326023 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 = 10.404326023 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 10.404326023 + 7.5 x = 10.404326023 + 7.5 Combine like terms: 10.404326023 + 7.5 = 17.904326023 x = 17.904326023 Simplifying x = 17.904326023Subproblem 2
x + -7.5 = -10.404326023 Simplifying x + -7.5 = -10.404326023 Reorder the terms: -7.5 + x = -10.404326023 Solving -7.5 + x = -10.404326023 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 = -10.404326023 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -10.404326023 + 7.5 x = -10.404326023 + 7.5 Combine like terms: -10.404326023 + 7.5 = -2.904326023 x = -2.904326023 Simplifying x = -2.904326023Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.904326023, -2.904326023}
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