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Simplifying -5x2 + -36x + 36 = 0 Reorder the terms: 36 + -36x + -5x2 = 0 Solving 36 + -36x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -7.2 + 7.2x + x2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + 7.2x + 7.2 + x2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + 7.2x + x2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + 7.2x + x2 = 0 + 7.2 7.2x + x2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 7.2x + x2 = 7.2 The x term is 7.2x. Take half its coefficient (3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. 7.2x + 12.96 + x2 = 7.2 + 12.96 Reorder the terms: 12.96 + 7.2x + x2 = 7.2 + 12.96 Combine like terms: 7.2 + 12.96 = 20.16 12.96 + 7.2x + x2 = 20.16 Factor a perfect square on the left side: (x + 3.6)(x + 3.6) = 20.16 Calculate the square root of the right side: 4.489988864 Break this problem into two subproblems by setting (x + 3.6) equal to 4.489988864 and -4.489988864.Subproblem 1
x + 3.6 = 4.489988864 Simplifying x + 3.6 = 4.489988864 Reorder the terms: 3.6 + x = 4.489988864 Solving 3.6 + x = 4.489988864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + x = 4.489988864 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + x = 4.489988864 + -3.6 x = 4.489988864 + -3.6 Combine like terms: 4.489988864 + -3.6 = 0.889988864 x = 0.889988864 Simplifying x = 0.889988864Subproblem 2
x + 3.6 = -4.489988864 Simplifying x + 3.6 = -4.489988864 Reorder the terms: 3.6 + x = -4.489988864 Solving 3.6 + x = -4.489988864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + x = -4.489988864 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + x = -4.489988864 + -3.6 x = -4.489988864 + -3.6 Combine like terms: -4.489988864 + -3.6 = -8.089988864 x = -8.089988864 Simplifying x = -8.089988864Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.889988864, -8.089988864}
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