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Simplifying 14 = 4x2 + 14x Reorder the terms: 14 = 14x + 4x2 Solving 14 = 14x + 4x2 Solving for variable 'x'. Reorder the terms: 14 + -14x + -4x2 = 14x + -14x + 4x2 + -4x2 Combine like terms: 14x + -14x = 0 14 + -14x + -4x2 = 0 + 4x2 + -4x2 14 + -14x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 14 + -14x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -7x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -7x + -2x2)' equal to zero and attempt to solve: Simplifying 7 + -7x + -2x2 = 0 Solving 7 + -7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -3.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 3.5x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 3.5x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 3.5x + x2 = 0 + 3.5 3.5x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 3.5x + x2 = 3.5 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 3.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 3.5 + 3.0625 Combine like terms: 3.5 + 3.0625 = 6.5625 3.0625 + 3.5x + x2 = 6.5625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (x + 1.75) equal to 2.561737691 and -2.561737691.Subproblem 1
x + 1.75 = 2.561737691 Simplifying x + 1.75 = 2.561737691 Reorder the terms: 1.75 + x = 2.561737691 Solving 1.75 + x = 2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 2.561737691 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 2.561737691 + -1.75 x = 2.561737691 + -1.75 Combine like terms: 2.561737691 + -1.75 = 0.811737691 x = 0.811737691 Simplifying x = 0.811737691Subproblem 2
x + 1.75 = -2.561737691 Simplifying x + 1.75 = -2.561737691 Reorder the terms: 1.75 + x = -2.561737691 Solving 1.75 + x = -2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -2.561737691 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -2.561737691 + -1.75 x = -2.561737691 + -1.75 Combine like terms: -2.561737691 + -1.75 = -4.311737691 x = -4.311737691 Simplifying x = -4.311737691Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.811737691, -4.311737691}Solution
x = {0.811737691, -4.311737691}
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