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Simplifying 35 = (2x + 5)(2x + 7) + -99 Reorder the terms: 35 = (5 + 2x)(2x + 7) + -99 Reorder the terms: 35 = (5 + 2x)(7 + 2x) + -99 Multiply (5 + 2x) * (7 + 2x) 35 = (5(7 + 2x) + 2x * (7 + 2x)) + -99 35 = ((7 * 5 + 2x * 5) + 2x * (7 + 2x)) + -99 35 = ((35 + 10x) + 2x * (7 + 2x)) + -99 35 = (35 + 10x + (7 * 2x + 2x * 2x)) + -99 35 = (35 + 10x + (14x + 4x2)) + -99 Combine like terms: 10x + 14x = 24x 35 = (35 + 24x + 4x2) + -99 Reorder the terms: 35 = 35 + -99 + 24x + 4x2 Combine like terms: 35 + -99 = -64 35 = -64 + 24x + 4x2 Solving 35 = -64 + 24x + 4x2 Solving for variable 'x'. Combine like terms: 35 + 64 = 99 99 + -24x + -4x2 = -64 + 24x + 4x2 + 64 + -24x + -4x2 Reorder the terms: 99 + -24x + -4x2 = -64 + 64 + 24x + -24x + 4x2 + -4x2 Combine like terms: -64 + 64 = 0 99 + -24x + -4x2 = 0 + 24x + -24x + 4x2 + -4x2 99 + -24x + -4x2 = 24x + -24x + 4x2 + -4x2 Combine like terms: 24x + -24x = 0 99 + -24x + -4x2 = 0 + 4x2 + -4x2 99 + -24x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 99 + -24x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -24.75 + 6x + x2 = 0 Move the constant term to the right: Add '24.75' to each side of the equation. -24.75 + 6x + 24.75 + x2 = 0 + 24.75 Reorder the terms: -24.75 + 24.75 + 6x + x2 = 0 + 24.75 Combine like terms: -24.75 + 24.75 = 0.00 0.00 + 6x + x2 = 0 + 24.75 6x + x2 = 0 + 24.75 Combine like terms: 0 + 24.75 = 24.75 6x + x2 = 24.75 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 24.75 + 9 Reorder the terms: 9 + 6x + x2 = 24.75 + 9 Combine like terms: 24.75 + 9 = 33.75 9 + 6x + x2 = 33.75 Factor a perfect square on the left side: (x + 3)(x + 3) = 33.75 Calculate the square root of the right side: 5.809475019 Break this problem into two subproblems by setting (x + 3) equal to 5.809475019 and -5.809475019.Subproblem 1
x + 3 = 5.809475019 Simplifying x + 3 = 5.809475019 Reorder the terms: 3 + x = 5.809475019 Solving 3 + x = 5.809475019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5.809475019 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.809475019 + -3 x = 5.809475019 + -3 Combine like terms: 5.809475019 + -3 = 2.809475019 x = 2.809475019 Simplifying x = 2.809475019Subproblem 2
x + 3 = -5.809475019 Simplifying x + 3 = -5.809475019 Reorder the terms: 3 + x = -5.809475019 Solving 3 + x = -5.809475019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5.809475019 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.809475019 + -3 x = -5.809475019 + -3 Combine like terms: -5.809475019 + -3 = -8.809475019 x = -8.809475019 Simplifying x = -8.809475019Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.809475019, -8.809475019}
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