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Simplifying 48x2 + 32x + -15 = 0 Reorder the terms: -15 + 32x + 48x2 = 0 Solving -15 + 32x + 48x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.3125 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + 0.6666666667x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + 0.6666666667x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + 0.6666666667x + x2 = 0 + 0.3125 0.6666666667x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 0.6666666667x + x2 = 0.3125 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 0.3125 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 0.3125 + 0.1111111112 Combine like terms: 0.3125 + 0.1111111112 = 0.4236111112 0.1111111112 + 0.6666666667x + x2 = 0.4236111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 0.4236111112 Calculate the square root of the right side: 0.65085414 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 0.65085414 and -0.65085414.Subproblem 1
x + 0.3333333334 = 0.65085414 Simplifying x + 0.3333333334 = 0.65085414 Reorder the terms: 0.3333333334 + x = 0.65085414 Solving 0.3333333334 + x = 0.65085414 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 0.65085414 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 0.65085414 + -0.3333333334 x = 0.65085414 + -0.3333333334 Combine like terms: 0.65085414 + -0.3333333334 = 0.3175208066 x = 0.3175208066 Simplifying x = 0.3175208066Subproblem 2
x + 0.3333333334 = -0.65085414 Simplifying x + 0.3333333334 = -0.65085414 Reorder the terms: 0.3333333334 + x = -0.65085414 Solving 0.3333333334 + x = -0.65085414 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -0.65085414 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -0.65085414 + -0.3333333334 x = -0.65085414 + -0.3333333334 Combine like terms: -0.65085414 + -0.3333333334 = -0.9841874734 x = -0.9841874734 Simplifying x = -0.9841874734Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3175208066, -0.9841874734}
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