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Simplifying 0 = -16x2 + 90x + -4 Reorder the terms: 0 = -4 + 90x + -16x2 Solving 0 = -4 + 90x + -16x2 Solving for variable 'x'. Combine like terms: 0 + 4 = 4 4 + -90x + 16x2 = -4 + 90x + -16x2 + 4 + -90x + 16x2 Reorder the terms: 4 + -90x + 16x2 = -4 + 4 + 90x + -90x + -16x2 + 16x2 Combine like terms: -4 + 4 = 0 4 + -90x + 16x2 = 0 + 90x + -90x + -16x2 + 16x2 4 + -90x + 16x2 = 90x + -90x + -16x2 + 16x2 Combine like terms: 90x + -90x = 0 4 + -90x + 16x2 = 0 + -16x2 + 16x2 4 + -90x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 4 + -90x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -45x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -45x + 8x2)' equal to zero and attempt to solve: Simplifying 2 + -45x + 8x2 = 0 Solving 2 + -45x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.25 + -5.625x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -5.625x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -5.625x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -5.625x + x2 = 0 + -0.25 -5.625x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -5.625x + x2 = -0.25 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 = -0.25 + 7.91015625 Reorder the terms: 7.91015625 + -5.625x + x2 = -0.25 + 7.91015625 Combine like terms: -0.25 + 7.91015625 = 7.66015625 7.91015625 + -5.625x + x2 = 7.66015625 Factor a perfect square on the left side: (x + -2.8125)(x + -2.8125) = 7.66015625 Calculate the square root of the right side: 2.767698728 Break this problem into two subproblems by setting (x + -2.8125) equal to 2.767698728 and -2.767698728.Subproblem 1
x + -2.8125 = 2.767698728 Simplifying x + -2.8125 = 2.767698728 Reorder the terms: -2.8125 + x = 2.767698728 Solving -2.8125 + x = 2.767698728 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 = 2.767698728 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = 2.767698728 + 2.8125 x = 2.767698728 + 2.8125 Combine like terms: 2.767698728 + 2.8125 = 5.580198728 x = 5.580198728 Simplifying x = 5.580198728Subproblem 2
x + -2.8125 = -2.767698728 Simplifying x + -2.8125 = -2.767698728 Reorder the terms: -2.8125 + x = -2.767698728 Solving -2.8125 + x = -2.767698728 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 = -2.767698728 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = -2.767698728 + 2.8125 x = -2.767698728 + 2.8125 Combine like terms: -2.767698728 + 2.8125 = 0.044801272 x = 0.044801272 Simplifying x = 0.044801272Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.580198728, 0.044801272}Solution
x = {5.580198728, 0.044801272}
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