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Simplifying 9x2 + 30x + 25 = x2 + 10x + 81 Reorder the terms: 25 + 30x + 9x2 = x2 + 10x + 81 Reorder the terms: 25 + 30x + 9x2 = 81 + 10x + x2 Solving 25 + 30x + 9x2 = 81 + 10x + x2 Solving for variable 'x'. Reorder the terms: 25 + -81 + 30x + -10x + 9x2 + -1x2 = 81 + 10x + x2 + -81 + -10x + -1x2 Combine like terms: 25 + -81 = -56 -56 + 30x + -10x + 9x2 + -1x2 = 81 + 10x + x2 + -81 + -10x + -1x2 Combine like terms: 30x + -10x = 20x -56 + 20x + 9x2 + -1x2 = 81 + 10x + x2 + -81 + -10x + -1x2 Combine like terms: 9x2 + -1x2 = 8x2 -56 + 20x + 8x2 = 81 + 10x + x2 + -81 + -10x + -1x2 Reorder the terms: -56 + 20x + 8x2 = 81 + -81 + 10x + -10x + x2 + -1x2 Combine like terms: 81 + -81 = 0 -56 + 20x + 8x2 = 0 + 10x + -10x + x2 + -1x2 -56 + 20x + 8x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 -56 + 20x + 8x2 = 0 + x2 + -1x2 -56 + 20x + 8x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -56 + 20x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-14 + 5x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-14 + 5x + 2x2)' equal to zero and attempt to solve: Simplifying -14 + 5x + 2x2 = 0 Solving -14 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7 + 2.5x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 2.5x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 2.5x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2.5x + x2 = 0 + 7 2.5x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 2.5x + x2 = 7 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 7 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 7 + 1.5625 Combine like terms: 7 + 1.5625 = 8.5625 1.5625 + 2.5x + x2 = 8.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (x + 1.25) equal to 2.926174978 and -2.926174978.Subproblem 1
x + 1.25 = 2.926174978 Simplifying x + 1.25 = 2.926174978 Reorder the terms: 1.25 + x = 2.926174978 Solving 1.25 + x = 2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.926174978 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.926174978 + -1.25 x = 2.926174978 + -1.25 Combine like terms: 2.926174978 + -1.25 = 1.676174978 x = 1.676174978 Simplifying x = 1.676174978Subproblem 2
x + 1.25 = -2.926174978 Simplifying x + 1.25 = -2.926174978 Reorder the terms: 1.25 + x = -2.926174978 Solving 1.25 + x = -2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.926174978 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.926174978 + -1.25 x = -2.926174978 + -1.25 Combine like terms: -2.926174978 + -1.25 = -4.176174978 x = -4.176174978 Simplifying x = -4.176174978Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.676174978, -4.176174978}Solution
x = {1.676174978, -4.176174978}
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