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Simplifying 7x + -21 + 7x + 21 = 8x2 + 8x + -72 Reorder the terms: -21 + 21 + 7x + 7x = 8x2 + 8x + -72 Combine like terms: -21 + 21 = 0 0 + 7x + 7x = 8x2 + 8x + -72 7x + 7x = 8x2 + 8x + -72 Combine like terms: 7x + 7x = 14x 14x = 8x2 + 8x + -72 Reorder the terms: 14x = -72 + 8x + 8x2 Solving 14x = -72 + 8x + 8x2 Solving for variable 'x'. Reorder the terms: 72 + 14x + -8x + -8x2 = -72 + 8x + 8x2 + 72 + -8x + -8x2 Combine like terms: 14x + -8x = 6x 72 + 6x + -8x2 = -72 + 8x + 8x2 + 72 + -8x + -8x2 Reorder the terms: 72 + 6x + -8x2 = -72 + 72 + 8x + -8x + 8x2 + -8x2 Combine like terms: -72 + 72 = 0 72 + 6x + -8x2 = 0 + 8x + -8x + 8x2 + -8x2 72 + 6x + -8x2 = 8x + -8x + 8x2 + -8x2 Combine like terms: 8x + -8x = 0 72 + 6x + -8x2 = 0 + 8x2 + -8x2 72 + 6x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 72 + 6x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(36 + 3x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(36 + 3x + -4x2)' equal to zero and attempt to solve: Simplifying 36 + 3x + -4x2 = 0 Solving 36 + 3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -9 + -0.75x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -0.75x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -0.75x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -0.75x + x2 = 0 + 9 -0.75x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -0.75x + x2 = 9 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 9 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 9 + 0.140625 Combine like terms: 9 + 0.140625 = 9.140625 0.140625 + -0.75x + x2 = 9.140625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 9.140625 Calculate the square root of the right side: 3.023346656 Break this problem into two subproblems by setting (x + -0.375) equal to 3.023346656 and -3.023346656.Subproblem 1
x + -0.375 = 3.023346656 Simplifying x + -0.375 = 3.023346656 Reorder the terms: -0.375 + x = 3.023346656 Solving -0.375 + x = 3.023346656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 3.023346656 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 3.023346656 + 0.375 x = 3.023346656 + 0.375 Combine like terms: 3.023346656 + 0.375 = 3.398346656 x = 3.398346656 Simplifying x = 3.398346656Subproblem 2
x + -0.375 = -3.023346656 Simplifying x + -0.375 = -3.023346656 Reorder the terms: -0.375 + x = -3.023346656 Solving -0.375 + x = -3.023346656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -3.023346656 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -3.023346656 + 0.375 x = -3.023346656 + 0.375 Combine like terms: -3.023346656 + 0.375 = -2.648346656 x = -2.648346656 Simplifying x = -2.648346656Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.398346656, -2.648346656}Solution
x = {3.398346656, -2.648346656}
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