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Simplifying 0 = 6x2 + 6x + -5 Reorder the terms: 0 = -5 + 6x + 6x2 Solving 0 = -5 + 6x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 5 = 5 5 + -6x + -6x2 = -5 + 6x + 6x2 + 5 + -6x + -6x2 Reorder the terms: 5 + -6x + -6x2 = -5 + 5 + 6x + -6x + 6x2 + -6x2 Combine like terms: -5 + 5 = 0 5 + -6x + -6x2 = 0 + 6x + -6x + 6x2 + -6x2 5 + -6x + -6x2 = 6x + -6x + 6x2 + -6x2 Combine like terms: 6x + -6x = 0 5 + -6x + -6x2 = 0 + 6x2 + -6x2 5 + -6x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 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 + x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + x + x2 = 0 + 0.8333333333 x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 x + x2 = 0.8333333333 The x term is x. 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. + 0.25 + x2 = 0.8333333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.8333333333 + 0.25 Combine like terms: 0.8333333333 + 0.25 = 1.0833333333 1.25 + 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 = 0.540833 x = 0.540833 Simplifying x = 0.540833Subproblem 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 = -1.540833 x = -1.540833 Simplifying x = -1.540833Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.540833, -1.540833}
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