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Simplifying 28x + 140 = 2x2 + 10 Reorder the terms: 140 + 28x = 2x2 + 10 Reorder the terms: 140 + 28x = 10 + 2x2 Solving 140 + 28x = 10 + 2x2 Solving for variable 'x'. Reorder the terms: 140 + -10 + 28x + -2x2 = 10 + 2x2 + -10 + -2x2 Combine like terms: 140 + -10 = 130 130 + 28x + -2x2 = 10 + 2x2 + -10 + -2x2 Reorder the terms: 130 + 28x + -2x2 = 10 + -10 + 2x2 + -2x2 Combine like terms: 10 + -10 = 0 130 + 28x + -2x2 = 0 + 2x2 + -2x2 130 + 28x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 130 + 28x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(65 + 14x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(65 + 14x + -1x2)' equal to zero and attempt to solve: Simplifying 65 + 14x + -1x2 = 0 Solving 65 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -65 + -14x + x2 = 0 Move the constant term to the right: Add '65' to each side of the equation. -65 + -14x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + -14x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + -14x + x2 = 0 + 65 -14x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 -14x + x2 = 65 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 = 65 + 49 Reorder the terms: 49 + -14x + x2 = 65 + 49 Combine like terms: 65 + 49 = 114 49 + -14x + x2 = 114 Factor a perfect square on the left side: (x + -7)(x + -7) = 114 Calculate the square root of the right side: 10.677078252 Break this problem into two subproblems by setting (x + -7) equal to 10.677078252 and -10.677078252.Subproblem 1
x + -7 = 10.677078252 Simplifying x + -7 = 10.677078252 Reorder the terms: -7 + x = 10.677078252 Solving -7 + x = 10.677078252 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 = 10.677078252 + 7 Combine like terms: -7 + 7 = 0 0 + x = 10.677078252 + 7 x = 10.677078252 + 7 Combine like terms: 10.677078252 + 7 = 17.677078252 x = 17.677078252 Simplifying x = 17.677078252Subproblem 2
x + -7 = -10.677078252 Simplifying x + -7 = -10.677078252 Reorder the terms: -7 + x = -10.677078252 Solving -7 + x = -10.677078252 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 = -10.677078252 + 7 Combine like terms: -7 + 7 = 0 0 + x = -10.677078252 + 7 x = -10.677078252 + 7 Combine like terms: -10.677078252 + 7 = -3.677078252 x = -3.677078252 Simplifying x = -3.677078252Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.677078252, -3.677078252}Solution
x = {17.677078252, -3.677078252}
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