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Simplifying 10 = 12x2 + 18x + -30x Reorder the terms: 10 = 18x + -30x + 12x2 Combine like terms: 18x + -30x = -12x 10 = -12x + 12x2 Solving 10 = -12x + 12x2 Solving for variable 'x'. Reorder the terms: 10 + 12x + -12x2 = -12x + 12x + 12x2 + -12x2 Combine like terms: -12x + 12x = 0 10 + 12x + -12x2 = 0 + 12x2 + -12x2 10 + 12x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 10 + 12x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 6x + -6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 6x + -6x2)' equal to zero and attempt to solve: Simplifying 5 + 6x + -6x2 = 0 Solving 5 + 6x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.8333333333 + -1x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -1x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -1x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + 0.8333333333 -1x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -1x + x2 = 0.8333333333 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.8333333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.8333333333 + 0.25 Combine like terms: 0.8333333333 + 0.25 = 1.0833333333 0.25 + -1x + x2 = 1.0833333333 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.0833333333 Calculate the square root of the right side: 1.040833 Break this problem into two subproblems by setting (x + -0.5) equal to 1.040833 and -1.040833.Subproblem 1
x + -0.5 = 1.040833 Simplifying x + -0.5 = 1.040833 Reorder the terms: -0.5 + x = 1.040833 Solving -0.5 + x = 1.040833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.040833 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.040833 + 0.5 x = 1.040833 + 0.5 Combine like terms: 1.040833 + 0.5 = 1.540833 x = 1.540833 Simplifying x = 1.540833Subproblem 2
x + -0.5 = -1.040833 Simplifying x + -0.5 = -1.040833 Reorder the terms: -0.5 + x = -1.040833 Solving -0.5 + x = -1.040833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.040833 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.040833 + 0.5 x = -1.040833 + 0.5 Combine like terms: -1.040833 + 0.5 = -0.540833 x = -0.540833 Simplifying x = -0.540833Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.540833, -0.540833}Solution
x = {1.540833, -0.540833}
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