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Simplifying -90x2 + -84x + 8 = 0 Reorder the terms: 8 + -84x + -90x2 = 0 Solving 8 + -84x + -90x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -42x + -45x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -42x + -45x2)' equal to zero and attempt to solve: Simplifying 4 + -42x + -45x2 = 0 Solving 4 + -42x + -45x2 = 0 Begin completing the square. Divide all terms by -45 the coefficient of the squared term: Divide each side by '-45'. -0.08888888889 + 0.9333333333x + x2 = 0 Move the constant term to the right: Add '0.08888888889' to each side of the equation. -0.08888888889 + 0.9333333333x + 0.08888888889 + x2 = 0 + 0.08888888889 Reorder the terms: -0.08888888889 + 0.08888888889 + 0.9333333333x + x2 = 0 + 0.08888888889 Combine like terms: -0.08888888889 + 0.08888888889 = 0.00000000000 0.00000000000 + 0.9333333333x + x2 = 0 + 0.08888888889 0.9333333333x + x2 = 0 + 0.08888888889 Combine like terms: 0 + 0.08888888889 = 0.08888888889 0.9333333333x + x2 = 0.08888888889 The x term is 0.9333333333x. Take half its coefficient (0.4666666667). Square it (0.2177777778) and add it to both sides. Add '0.2177777778' to each side of the equation. 0.9333333333x + 0.2177777778 + x2 = 0.08888888889 + 0.2177777778 Reorder the terms: 0.2177777778 + 0.9333333333x + x2 = 0.08888888889 + 0.2177777778 Combine like terms: 0.08888888889 + 0.2177777778 = 0.30666666669 0.2177777778 + 0.9333333333x + x2 = 0.30666666669 Factor a perfect square on the left side: (x + 0.4666666667)(x + 0.4666666667) = 0.30666666669 Calculate the square root of the right side: 0.553774924 Break this problem into two subproblems by setting (x + 0.4666666667) equal to 0.553774924 and -0.553774924.Subproblem 1
x + 0.4666666667 = 0.553774924 Simplifying x + 0.4666666667 = 0.553774924 Reorder the terms: 0.4666666667 + x = 0.553774924 Solving 0.4666666667 + x = 0.553774924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4666666667' to each side of the equation. 0.4666666667 + -0.4666666667 + x = 0.553774924 + -0.4666666667 Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000 0.0000000000 + x = 0.553774924 + -0.4666666667 x = 0.553774924 + -0.4666666667 Combine like terms: 0.553774924 + -0.4666666667 = 0.0871082573 x = 0.0871082573 Simplifying x = 0.0871082573Subproblem 2
x + 0.4666666667 = -0.553774924 Simplifying x + 0.4666666667 = -0.553774924 Reorder the terms: 0.4666666667 + x = -0.553774924 Solving 0.4666666667 + x = -0.553774924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4666666667' to each side of the equation. 0.4666666667 + -0.4666666667 + x = -0.553774924 + -0.4666666667 Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000 0.0000000000 + x = -0.553774924 + -0.4666666667 x = -0.553774924 + -0.4666666667 Combine like terms: -0.553774924 + -0.4666666667 = -1.0204415907 x = -1.0204415907 Simplifying x = -1.0204415907Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0871082573, -1.0204415907}Solution
x = {0.0871082573, -1.0204415907}
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