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Simplifying 4x2 + 14x + -112 = 0 Reorder the terms: -112 + 14x + 4x2 = 0 Solving -112 + 14x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-56 + 7x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-56 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying -56 + 7x + 2x2 = 0 Solving -56 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -28 + 3.5x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + 3.5x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 3.5x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 3.5x + x2 = 0 + 28 3.5x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 3.5x + x2 = 28 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 = 28 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 28 + 3.0625 Combine like terms: 28 + 3.0625 = 31.0625 3.0625 + 3.5x + x2 = 31.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 31.0625 Calculate the square root of the right side: 5.573374202 Break this problem into two subproblems by setting (x + 1.75) equal to 5.573374202 and -5.573374202.Subproblem 1
x + 1.75 = 5.573374202 Simplifying x + 1.75 = 5.573374202 Reorder the terms: 1.75 + x = 5.573374202 Solving 1.75 + x = 5.573374202 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 = 5.573374202 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 5.573374202 + -1.75 x = 5.573374202 + -1.75 Combine like terms: 5.573374202 + -1.75 = 3.823374202 x = 3.823374202 Simplifying x = 3.823374202Subproblem 2
x + 1.75 = -5.573374202 Simplifying x + 1.75 = -5.573374202 Reorder the terms: 1.75 + x = -5.573374202 Solving 1.75 + x = -5.573374202 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 = -5.573374202 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -5.573374202 + -1.75 x = -5.573374202 + -1.75 Combine like terms: -5.573374202 + -1.75 = -7.323374202 x = -7.323374202 Simplifying x = -7.323374202Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.823374202, -7.323374202}Solution
x = {3.823374202, -7.323374202}
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