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Simplifying 28x2 + 102x + -112 = 0 Reorder the terms: -112 + 102x + 28x2 = 0 Solving -112 + 102x + 28x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-56 + 51x + 14x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-56 + 51x + 14x2)' equal to zero and attempt to solve: Simplifying -56 + 51x + 14x2 = 0 Solving -56 + 51x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -4 + 3.642857143x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 3.642857143x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 3.642857143x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3.642857143x + x2 = 0 + 4 3.642857143x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 3.642857143x + x2 = 4 The x term is 3.642857143x. Take half its coefficient (1.821428572). Square it (3.317602043) and add it to both sides. Add '3.317602043' to each side of the equation. 3.642857143x + 3.317602043 + x2 = 4 + 3.317602043 Reorder the terms: 3.317602043 + 3.642857143x + x2 = 4 + 3.317602043 Combine like terms: 4 + 3.317602043 = 7.317602043 3.317602043 + 3.642857143x + x2 = 7.317602043 Factor a perfect square on the left side: (x + 1.821428572)(x + 1.821428572) = 7.317602043 Calculate the square root of the right side: 2.70510666 Break this problem into two subproblems by setting (x + 1.821428572) equal to 2.70510666 and -2.70510666.Subproblem 1
x + 1.821428572 = 2.70510666 Simplifying x + 1.821428572 = 2.70510666 Reorder the terms: 1.821428572 + x = 2.70510666 Solving 1.821428572 + x = 2.70510666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.821428572' to each side of the equation. 1.821428572 + -1.821428572 + x = 2.70510666 + -1.821428572 Combine like terms: 1.821428572 + -1.821428572 = 0.000000000 0.000000000 + x = 2.70510666 + -1.821428572 x = 2.70510666 + -1.821428572 Combine like terms: 2.70510666 + -1.821428572 = 0.883678088 x = 0.883678088 Simplifying x = 0.883678088Subproblem 2
x + 1.821428572 = -2.70510666 Simplifying x + 1.821428572 = -2.70510666 Reorder the terms: 1.821428572 + x = -2.70510666 Solving 1.821428572 + x = -2.70510666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.821428572' to each side of the equation. 1.821428572 + -1.821428572 + x = -2.70510666 + -1.821428572 Combine like terms: 1.821428572 + -1.821428572 = 0.000000000 0.000000000 + x = -2.70510666 + -1.821428572 x = -2.70510666 + -1.821428572 Combine like terms: -2.70510666 + -1.821428572 = -4.526535232 x = -4.526535232 Simplifying x = -4.526535232Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.883678088, -4.526535232}Solution
x = {0.883678088, -4.526535232}
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