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Simplifying 4x + 6x2 + 12x = 14x2 + -10x + -30 Reorder the terms: 4x + 12x + 6x2 = 14x2 + -10x + -30 Combine like terms: 4x + 12x = 16x 16x + 6x2 = 14x2 + -10x + -30 Reorder the terms: 16x + 6x2 = -30 + -10x + 14x2 Solving 16x + 6x2 = -30 + -10x + 14x2 Solving for variable 'x'. Reorder the terms: 30 + 16x + 10x + 6x2 + -14x2 = -30 + -10x + 14x2 + 30 + 10x + -14x2 Combine like terms: 16x + 10x = 26x 30 + 26x + 6x2 + -14x2 = -30 + -10x + 14x2 + 30 + 10x + -14x2 Combine like terms: 6x2 + -14x2 = -8x2 30 + 26x + -8x2 = -30 + -10x + 14x2 + 30 + 10x + -14x2 Reorder the terms: 30 + 26x + -8x2 = -30 + 30 + -10x + 10x + 14x2 + -14x2 Combine like terms: -30 + 30 = 0 30 + 26x + -8x2 = 0 + -10x + 10x + 14x2 + -14x2 30 + 26x + -8x2 = -10x + 10x + 14x2 + -14x2 Combine like terms: -10x + 10x = 0 30 + 26x + -8x2 = 0 + 14x2 + -14x2 30 + 26x + -8x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 30 + 26x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 13x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + 13x + -4x2)' equal to zero and attempt to solve: Simplifying 15 + 13x + -4x2 = 0 Solving 15 + 13x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -3.75 + -3.25x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -3.25x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -3.25x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -3.25x + x2 = 0 + 3.75 -3.25x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -3.25x + x2 = 3.75 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = 3.75 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = 3.75 + 2.640625 Combine like terms: 3.75 + 2.640625 = 6.390625 2.640625 + -3.25x + x2 = 6.390625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 6.390625 Calculate the square root of the right side: 2.527968552 Break this problem into two subproblems by setting (x + -1.625) equal to 2.527968552 and -2.527968552.Subproblem 1
x + -1.625 = 2.527968552 Simplifying x + -1.625 = 2.527968552 Reorder the terms: -1.625 + x = 2.527968552 Solving -1.625 + x = 2.527968552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 2.527968552 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 2.527968552 + 1.625 x = 2.527968552 + 1.625 Combine like terms: 2.527968552 + 1.625 = 4.152968552 x = 4.152968552 Simplifying x = 4.152968552Subproblem 2
x + -1.625 = -2.527968552 Simplifying x + -1.625 = -2.527968552 Reorder the terms: -1.625 + x = -2.527968552 Solving -1.625 + x = -2.527968552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -2.527968552 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -2.527968552 + 1.625 x = -2.527968552 + 1.625 Combine like terms: -2.527968552 + 1.625 = -0.902968552 x = -0.902968552 Simplifying x = -0.902968552Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.152968552, -0.902968552}Solution
x = {4.152968552, -0.902968552}
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