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Simplifying 12x2 + 15x + -4 = 0 Reorder the terms: -4 + 15x + 12x2 = 0 Solving -4 + 15x + 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'. -0.3333333333 + 1.25x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 1.25x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 1.25x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 1.25x + x2 = 0 + 0.3333333333 1.25x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 1.25x + x2 = 0.3333333333 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 0.3333333333 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 0.3333333333 + 0.390625 Combine like terms: 0.3333333333 + 0.390625 = 0.7239583333 0.390625 + 1.25x + x2 = 0.7239583333 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 0.7239583333 Calculate the square root of the right side: 0.850857411 Break this problem into two subproblems by setting (x + 0.625) equal to 0.850857411 and -0.850857411.Subproblem 1
x + 0.625 = 0.850857411 Simplifying x + 0.625 = 0.850857411 Reorder the terms: 0.625 + x = 0.850857411 Solving 0.625 + x = 0.850857411 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 0.850857411 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 0.850857411 + -0.625 x = 0.850857411 + -0.625 Combine like terms: 0.850857411 + -0.625 = 0.225857411 x = 0.225857411 Simplifying x = 0.225857411Subproblem 2
x + 0.625 = -0.850857411 Simplifying x + 0.625 = -0.850857411 Reorder the terms: 0.625 + x = -0.850857411 Solving 0.625 + x = -0.850857411 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -0.850857411 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -0.850857411 + -0.625 x = -0.850857411 + -0.625 Combine like terms: -0.850857411 + -0.625 = -1.475857411 x = -1.475857411 Simplifying x = -1.475857411Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.225857411, -1.475857411}
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