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Simplifying 10x2 + -6x + -6 = 0 Reorder the terms: -6 + -6x + 10x2 = 0 Solving -6 + -6x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -3x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -3x + 5x2)' equal to zero and attempt to solve: Simplifying -3 + -3x + 5x2 = 0 Solving -3 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -0.6x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -0.6x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -0.6x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -0.6x + x2 = 0 + 0.6 -0.6x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -0.6x + x2 = 0.6 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 0.6 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 0.6 + 0.09 Combine like terms: 0.6 + 0.09 = 0.69 0.09 + -0.6x + x2 = 0.69 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 0.69 Calculate the square root of the right side: 0.830662386 Break this problem into two subproblems by setting (x + -0.3) equal to 0.830662386 and -0.830662386.Subproblem 1
x + -0.3 = 0.830662386 Simplifying x + -0.3 = 0.830662386 Reorder the terms: -0.3 + x = 0.830662386 Solving -0.3 + x = 0.830662386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 0.830662386 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 0.830662386 + 0.3 x = 0.830662386 + 0.3 Combine like terms: 0.830662386 + 0.3 = 1.130662386 x = 1.130662386 Simplifying x = 1.130662386Subproblem 2
x + -0.3 = -0.830662386 Simplifying x + -0.3 = -0.830662386 Reorder the terms: -0.3 + x = -0.830662386 Solving -0.3 + x = -0.830662386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -0.830662386 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -0.830662386 + 0.3 x = -0.830662386 + 0.3 Combine like terms: -0.830662386 + 0.3 = -0.530662386 x = -0.530662386 Simplifying x = -0.530662386Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.130662386, -0.530662386}Solution
x = {1.130662386, -0.530662386}
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