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Simplifying -2x2 + 30x + 225 = 0 Reorder the terms: 225 + 30x + -2x2 = 0 Solving 225 + 30x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -112.5 + -15x + x2 = 0 Move the constant term to the right: Add '112.5' to each side of the equation. -112.5 + -15x + 112.5 + x2 = 0 + 112.5 Reorder the terms: -112.5 + 112.5 + -15x + x2 = 0 + 112.5 Combine like terms: -112.5 + 112.5 = 0.0 0.0 + -15x + x2 = 0 + 112.5 -15x + x2 = 0 + 112.5 Combine like terms: 0 + 112.5 = 112.5 -15x + x2 = 112.5 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 = 112.5 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 112.5 + 56.25 Combine like terms: 112.5 + 56.25 = 168.75 56.25 + -15x + x2 = 168.75 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 168.75 Calculate the square root of the right side: 12.990381057 Break this problem into two subproblems by setting (x + -7.5) equal to 12.990381057 and -12.990381057.Subproblem 1
x + -7.5 = 12.990381057 Simplifying x + -7.5 = 12.990381057 Reorder the terms: -7.5 + x = 12.990381057 Solving -7.5 + x = 12.990381057 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 = 12.990381057 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 12.990381057 + 7.5 x = 12.990381057 + 7.5 Combine like terms: 12.990381057 + 7.5 = 20.490381057 x = 20.490381057 Simplifying x = 20.490381057Subproblem 2
x + -7.5 = -12.990381057 Simplifying x + -7.5 = -12.990381057 Reorder the terms: -7.5 + x = -12.990381057 Solving -7.5 + x = -12.990381057 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 = -12.990381057 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -12.990381057 + 7.5 x = -12.990381057 + 7.5 Combine like terms: -12.990381057 + 7.5 = -5.490381057 x = -5.490381057 Simplifying x = -5.490381057Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.490381057, -5.490381057}
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