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Simplifying 12x2 + 12x + -25 = 0 Reorder the terms: -25 + 12x + 12x2 = 0 Solving -25 + 12x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -2.083333333 + x + x2 = 0 Move the constant term to the right: Add '2.083333333' to each side of the equation. -2.083333333 + x + 2.083333333 + x2 = 0 + 2.083333333 Reorder the terms: -2.083333333 + 2.083333333 + x + x2 = 0 + 2.083333333 Combine like terms: -2.083333333 + 2.083333333 = 0.000000000 0.000000000 + x + x2 = 0 + 2.083333333 x + x2 = 0 + 2.083333333 Combine like terms: 0 + 2.083333333 = 2.083333333 x + x2 = 2.083333333 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 = 2.083333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 2.083333333 + 0.25 Combine like terms: 2.083333333 + 0.25 = 2.333333333 1.25 + x2 = 2.333333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.333333333 Calculate the square root of the right side: 1.527525232 Break this problem into two subproblems by setting (x + 0.5) equal to 1.527525232 and -1.527525232.Subproblem 1
x + 0.5 = 1.527525232 Simplifying x + 0.5 = 1.527525232 Reorder the terms: 0.5 + x = 1.527525232 Solving 0.5 + x = 1.527525232 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 = 1.527525232 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.527525232 + -0.5 x = 1.527525232 + -0.5 Combine like terms: 1.527525232 + -0.5 = 1.027525232 x = 1.027525232 Simplifying x = 1.027525232Subproblem 2
x + 0.5 = -1.527525232 Simplifying x + 0.5 = -1.527525232 Reorder the terms: 0.5 + x = -1.527525232 Solving 0.5 + x = -1.527525232 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 = -1.527525232 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.527525232 + -0.5 x = -1.527525232 + -0.5 Combine like terms: -1.527525232 + -0.5 = -2.027525232 x = -2.027525232 Simplifying x = -2.027525232Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.027525232, -2.027525232}
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