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Simplifying 8x2 + -48 + -10x = 0 Reorder the terms: -48 + -10x + 8x2 = 0 Solving -48 + -10x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + -5x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-24 + -5x + 4x2)' equal to zero and attempt to solve: Simplifying -24 + -5x + 4x2 = 0 Solving -24 + -5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6 + -1.25x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -1.25x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -1.25x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1.25x + x2 = 0 + 6 -1.25x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -1.25x + x2 = 6 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 = 6 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 6 + 0.390625 Combine like terms: 6 + 0.390625 = 6.390625 0.390625 + -1.25x + x2 = 6.390625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 6.390625 Calculate the square root of the right side: 2.527968552 Break this problem into two subproblems by setting (x + -0.625) equal to 2.527968552 and -2.527968552.Subproblem 1
x + -0.625 = 2.527968552 Simplifying x + -0.625 = 2.527968552 Reorder the terms: -0.625 + x = 2.527968552 Solving -0.625 + x = 2.527968552 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 = 2.527968552 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 2.527968552 + 0.625 x = 2.527968552 + 0.625 Combine like terms: 2.527968552 + 0.625 = 3.152968552 x = 3.152968552 Simplifying x = 3.152968552Subproblem 2
x + -0.625 = -2.527968552 Simplifying x + -0.625 = -2.527968552 Reorder the terms: -0.625 + x = -2.527968552 Solving -0.625 + x = -2.527968552 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 = -2.527968552 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -2.527968552 + 0.625 x = -2.527968552 + 0.625 Combine like terms: -2.527968552 + 0.625 = -1.902968552 x = -1.902968552 Simplifying x = -1.902968552Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.152968552, -1.902968552}Solution
x = {3.152968552, -1.902968552}
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