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Simplifying 4x2 = 6x + 14 Reorder the terms: 4x2 = 14 + 6x Solving 4x2 = 14 + 6x Solving for variable 'x'. Reorder the terms: -14 + -6x + 4x2 = 14 + 6x + -14 + -6x Reorder the terms: -14 + -6x + 4x2 = 14 + -14 + 6x + -6x Combine like terms: 14 + -14 = 0 -14 + -6x + 4x2 = 0 + 6x + -6x -14 + -6x + 4x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -14 + -6x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -3x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -3x + 2x2)' equal to zero and attempt to solve: Simplifying -7 + -3x + 2x2 = 0 Solving -7 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -1.5x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -1.5x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -1.5x + x2 = 0 + 3.5 -1.5x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -1.5x + x2 = 3.5 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 3.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 3.5 + 0.5625 Combine like terms: 3.5 + 0.5625 = 4.0625 0.5625 + -1.5x + x2 = 4.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (x + -0.75) equal to 2.015564437 and -2.015564437.Subproblem 1
x + -0.75 = 2.015564437 Simplifying x + -0.75 = 2.015564437 Reorder the terms: -0.75 + x = 2.015564437 Solving -0.75 + x = 2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 2.015564437 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.015564437 + 0.75 x = 2.015564437 + 0.75 Combine like terms: 2.015564437 + 0.75 = 2.765564437 x = 2.765564437 Simplifying x = 2.765564437Subproblem 2
x + -0.75 = -2.015564437 Simplifying x + -0.75 = -2.015564437 Reorder the terms: -0.75 + x = -2.015564437 Solving -0.75 + x = -2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -2.015564437 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.015564437 + 0.75 x = -2.015564437 + 0.75 Combine like terms: -2.015564437 + 0.75 = -1.265564437 x = -1.265564437 Simplifying x = -1.265564437Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.765564437, -1.265564437}Solution
x = {2.765564437, -1.265564437}
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