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Simplifying 0 = -16x2 + 224x + 168 Reorder the terms: 0 = 168 + 224x + -16x2 Solving 0 = 168 + 224x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -168 = -168 -168 + -224x + 16x2 = 168 + 224x + -16x2 + -168 + -224x + 16x2 Reorder the terms: -168 + -224x + 16x2 = 168 + -168 + 224x + -224x + -16x2 + 16x2 Combine like terms: 168 + -168 = 0 -168 + -224x + 16x2 = 0 + 224x + -224x + -16x2 + 16x2 -168 + -224x + 16x2 = 224x + -224x + -16x2 + 16x2 Combine like terms: 224x + -224x = 0 -168 + -224x + 16x2 = 0 + -16x2 + 16x2 -168 + -224x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -168 + -224x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-21 + -28x + 2x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-21 + -28x + 2x2)' equal to zero and attempt to solve: Simplifying -21 + -28x + 2x2 = 0 Solving -21 + -28x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + -14x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + -14x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + -14x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + -14x + x2 = 0 + 10.5 -14x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 -14x + x2 = 10.5 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 10.5 + 49 Reorder the terms: 49 + -14x + x2 = 10.5 + 49 Combine like terms: 10.5 + 49 = 59.5 49 + -14x + x2 = 59.5 Factor a perfect square on the left side: (x + -7)(x + -7) = 59.5 Calculate the square root of the right side: 7.71362431 Break this problem into two subproblems by setting (x + -7) equal to 7.71362431 and -7.71362431.Subproblem 1
x + -7 = 7.71362431 Simplifying x + -7 = 7.71362431 Reorder the terms: -7 + x = 7.71362431 Solving -7 + x = 7.71362431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 7.71362431 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.71362431 + 7 x = 7.71362431 + 7 Combine like terms: 7.71362431 + 7 = 14.71362431 x = 14.71362431 Simplifying x = 14.71362431Subproblem 2
x + -7 = -7.71362431 Simplifying x + -7 = -7.71362431 Reorder the terms: -7 + x = -7.71362431 Solving -7 + x = -7.71362431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -7.71362431 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.71362431 + 7 x = -7.71362431 + 7 Combine like terms: -7.71362431 + 7 = -0.71362431 x = -0.71362431 Simplifying x = -0.71362431Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.71362431, -0.71362431}Solution
x = {14.71362431, -0.71362431}
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