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Simplifying -8 = 30x2 + 57x Reorder the terms: -8 = 57x + 30x2 Solving -8 = 57x + 30x2 Solving for variable 'x'. Reorder the terms: -8 + -57x + -30x2 = 57x + -57x + 30x2 + -30x2 Combine like terms: 57x + -57x = 0 -8 + -57x + -30x2 = 0 + 30x2 + -30x2 -8 + -57x + -30x2 = 30x2 + -30x2 Combine like terms: 30x2 + -30x2 = 0 -8 + -57x + -30x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 57x + 30x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 57x + 30x2)' equal to zero and attempt to solve: Simplifying 8 + 57x + 30x2 = 0 Solving 8 + 57x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. 0.2666666667 + 1.9x + x2 = 0.0 Move the constant term to the right: Add '-0.2666666667' to each side of the equation. 0.2666666667 + 1.9x + -0.2666666667 + x2 = 0.0 + -0.2666666667 Reorder the terms: 0.2666666667 + -0.2666666667 + 1.9x + x2 = 0.0 + -0.2666666667 Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000 0.0000000000 + 1.9x + x2 = 0.0 + -0.2666666667 1.9x + x2 = 0.0 + -0.2666666667 Combine like terms: 0.0 + -0.2666666667 = -0.2666666667 1.9x + x2 = -0.2666666667 The x term is 1.9x. Take half its coefficient (0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. 1.9x + 0.9025 + x2 = -0.2666666667 + 0.9025 Reorder the terms: 0.9025 + 1.9x + x2 = -0.2666666667 + 0.9025 Combine like terms: -0.2666666667 + 0.9025 = 0.6358333333 0.9025 + 1.9x + x2 = 0.6358333333 Factor a perfect square on the left side: (x + 0.95)(x + 0.95) = 0.6358333333 Calculate the square root of the right side: 0.797391581 Break this problem into two subproblems by setting (x + 0.95) equal to 0.797391581 and -0.797391581.Subproblem 1
x + 0.95 = 0.797391581 Simplifying x + 0.95 = 0.797391581 Reorder the terms: 0.95 + x = 0.797391581 Solving 0.95 + x = 0.797391581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.95' to each side of the equation. 0.95 + -0.95 + x = 0.797391581 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + x = 0.797391581 + -0.95 x = 0.797391581 + -0.95 Combine like terms: 0.797391581 + -0.95 = -0.152608419 x = -0.152608419 Simplifying x = -0.152608419Subproblem 2
x + 0.95 = -0.797391581 Simplifying x + 0.95 = -0.797391581 Reorder the terms: 0.95 + x = -0.797391581 Solving 0.95 + x = -0.797391581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.95' to each side of the equation. 0.95 + -0.95 + x = -0.797391581 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + x = -0.797391581 + -0.95 x = -0.797391581 + -0.95 Combine like terms: -0.797391581 + -0.95 = -1.747391581 x = -1.747391581 Simplifying x = -1.747391581Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.152608419, -1.747391581}Solution
x = {-0.152608419, -1.747391581}
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