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Simplifying -1x2 + 15x + 63 = 0 Reorder the terms: 63 + 15x + -1x2 = 0 Solving 63 + 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'. -63 + -15x + x2 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + -15x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + -15x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + -15x + x2 = 0 + 63 -15x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 -15x + x2 = 63 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 = 63 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 63 + 56.25 Combine like terms: 63 + 56.25 = 119.25 56.25 + -15x + x2 = 119.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 119.25 Calculate the square root of the right side: 10.920164834 Break this problem into two subproblems by setting (x + -7.5) equal to 10.920164834 and -10.920164834.Subproblem 1
x + -7.5 = 10.920164834 Simplifying x + -7.5 = 10.920164834 Reorder the terms: -7.5 + x = 10.920164834 Solving -7.5 + x = 10.920164834 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 = 10.920164834 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 10.920164834 + 7.5 x = 10.920164834 + 7.5 Combine like terms: 10.920164834 + 7.5 = 18.420164834 x = 18.420164834 Simplifying x = 18.420164834Subproblem 2
x + -7.5 = -10.920164834 Simplifying x + -7.5 = -10.920164834 Reorder the terms: -7.5 + x = -10.920164834 Solving -7.5 + x = -10.920164834 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 = -10.920164834 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -10.920164834 + 7.5 x = -10.920164834 + 7.5 Combine like terms: -10.920164834 + 7.5 = -3.420164834 x = -3.420164834 Simplifying x = -3.420164834Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.420164834, -3.420164834}
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