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Simplifying 12x2 + 15x + -8 = 0 Reorder the terms: -8 + 15x + 12x2 = 0 Solving -8 + 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'. -0.6666666667 + 1.25x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 1.25x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 1.25x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 1.25x + x2 = 0 + 0.6666666667 1.25x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 1.25x + x2 = 0.6666666667 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 = 0.6666666667 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 0.6666666667 + 0.390625 Combine like terms: 0.6666666667 + 0.390625 = 1.0572916667 0.390625 + 1.25x + x2 = 1.0572916667 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 1.0572916667 Calculate the square root of the right side: 1.02824689 Break this problem into two subproblems by setting (x + 0.625) equal to 1.02824689 and -1.02824689.Subproblem 1
x + 0.625 = 1.02824689 Simplifying x + 0.625 = 1.02824689 Reorder the terms: 0.625 + x = 1.02824689 Solving 0.625 + x = 1.02824689 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 = 1.02824689 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 1.02824689 + -0.625 x = 1.02824689 + -0.625 Combine like terms: 1.02824689 + -0.625 = 0.40324689 x = 0.40324689 Simplifying x = 0.40324689Subproblem 2
x + 0.625 = -1.02824689 Simplifying x + 0.625 = -1.02824689 Reorder the terms: 0.625 + x = -1.02824689 Solving 0.625 + x = -1.02824689 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 = -1.02824689 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -1.02824689 + -0.625 x = -1.02824689 + -0.625 Combine like terms: -1.02824689 + -0.625 = -1.65324689 x = -1.65324689 Simplifying x = -1.65324689Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.40324689, -1.65324689}
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