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Simplifying 0 = -16x2 + 90x + 2 Reorder the terms: 0 = 2 + 90x + -16x2 Solving 0 = 2 + 90x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + -90x + 16x2 = 2 + 90x + -16x2 + -2 + -90x + 16x2 Reorder the terms: -2 + -90x + 16x2 = 2 + -2 + 90x + -90x + -16x2 + 16x2 Combine like terms: 2 + -2 = 0 -2 + -90x + 16x2 = 0 + 90x + -90x + -16x2 + 16x2 -2 + -90x + 16x2 = 90x + -90x + -16x2 + 16x2 Combine like terms: 90x + -90x = 0 -2 + -90x + 16x2 = 0 + -16x2 + 16x2 -2 + -90x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -2 + -90x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -45x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -45x + 8x2)' equal to zero and attempt to solve: Simplifying -1 + -45x + 8x2 = 0 Solving -1 + -45x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -5.625x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -5.625x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -5.625x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -5.625x + x2 = 0 + 0.125 -5.625x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -5.625x + x2 = 0.125 The x term is -5.625x. Take half its coefficient (-2.8125). Square it (7.91015625) and add it to both sides. Add '7.91015625' to each side of the equation. -5.625x + 7.91015625 + x2 = 0.125 + 7.91015625 Reorder the terms: 7.91015625 + -5.625x + x2 = 0.125 + 7.91015625 Combine like terms: 0.125 + 7.91015625 = 8.03515625 7.91015625 + -5.625x + x2 = 8.03515625 Factor a perfect square on the left side: (x + -2.8125)(x + -2.8125) = 8.03515625 Calculate the square root of the right side: 2.834635118 Break this problem into two subproblems by setting (x + -2.8125) equal to 2.834635118 and -2.834635118.Subproblem 1
x + -2.8125 = 2.834635118 Simplifying x + -2.8125 = 2.834635118 Reorder the terms: -2.8125 + x = 2.834635118 Solving -2.8125 + x = 2.834635118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + x = 2.834635118 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = 2.834635118 + 2.8125 x = 2.834635118 + 2.8125 Combine like terms: 2.834635118 + 2.8125 = 5.647135118 x = 5.647135118 Simplifying x = 5.647135118Subproblem 2
x + -2.8125 = -2.834635118 Simplifying x + -2.8125 = -2.834635118 Reorder the terms: -2.8125 + x = -2.834635118 Solving -2.8125 + x = -2.834635118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + x = -2.834635118 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = -2.834635118 + 2.8125 x = -2.834635118 + 2.8125 Combine like terms: -2.834635118 + 2.8125 = -0.022135118 x = -0.022135118 Simplifying x = -0.022135118Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.647135118, -0.022135118}Solution
x = {5.647135118, -0.022135118}
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