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Simplifying 4x2 + 12x + -14 = 0 Reorder the terms: -14 + 12x + 4x2 = 0 Solving -14 + 12x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 6x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 6x + 2x2)' equal to zero and attempt to solve: Simplifying -7 + 6x + 2x2 = 0 Solving -7 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 3x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 3x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 3x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 3x + x2 = 0 + 3.5 3x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 3x + x2 = 3.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 3.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 3.5 + 2.25 Combine like terms: 3.5 + 2.25 = 5.75 2.25 + 3x + x2 = 5.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 5.75 Calculate the square root of the right side: 2.397915762 Break this problem into two subproblems by setting (x + 1.5) equal to 2.397915762 and -2.397915762.Subproblem 1
x + 1.5 = 2.397915762 Simplifying x + 1.5 = 2.397915762 Reorder the terms: 1.5 + x = 2.397915762 Solving 1.5 + x = 2.397915762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.397915762 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.397915762 + -1.5 x = 2.397915762 + -1.5 Combine like terms: 2.397915762 + -1.5 = 0.897915762 x = 0.897915762 Simplifying x = 0.897915762Subproblem 2
x + 1.5 = -2.397915762 Simplifying x + 1.5 = -2.397915762 Reorder the terms: 1.5 + x = -2.397915762 Solving 1.5 + x = -2.397915762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.397915762 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.397915762 + -1.5 x = -2.397915762 + -1.5 Combine like terms: -2.397915762 + -1.5 = -3.897915762 x = -3.897915762 Simplifying x = -3.897915762Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.897915762, -3.897915762}Solution
x = {0.897915762, -3.897915762}
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