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Simplifying 100 + -2x2 + 4x = 32 Reorder the terms: 100 + 4x + -2x2 = 32 Solving 100 + 4x + -2x2 = 32 Solving for variable 'x'. Reorder the terms: 100 + -32 + 4x + -2x2 = 32 + -32 Combine like terms: 100 + -32 = 68 68 + 4x + -2x2 = 32 + -32 Combine like terms: 32 + -32 = 0 68 + 4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(34 + 2x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(34 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying 34 + 2x + -1x2 = 0 Solving 34 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -34 + -2x + x2 = 0 Move the constant term to the right: Add '34' to each side of the equation. -34 + -2x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + -2x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + -2x + x2 = 0 + 34 -2x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 -2x + x2 = 34 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 34 + 1 Reorder the terms: 1 + -2x + x2 = 34 + 1 Combine like terms: 34 + 1 = 35 1 + -2x + x2 = 35 Factor a perfect square on the left side: (x + -1)(x + -1) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (x + -1) equal to 5.916079783 and -5.916079783.Subproblem 1
x + -1 = 5.916079783 Simplifying x + -1 = 5.916079783 Reorder the terms: -1 + x = 5.916079783 Solving -1 + x = 5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 5.916079783 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.916079783 + 1 x = 5.916079783 + 1 Combine like terms: 5.916079783 + 1 = 6.916079783 x = 6.916079783 Simplifying x = 6.916079783Subproblem 2
x + -1 = -5.916079783 Simplifying x + -1 = -5.916079783 Reorder the terms: -1 + x = -5.916079783 Solving -1 + x = -5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -5.916079783 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.916079783 + 1 x = -5.916079783 + 1 Combine like terms: -5.916079783 + 1 = -4.916079783 x = -4.916079783 Simplifying x = -4.916079783Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.916079783, -4.916079783}Solution
x = {6.916079783, -4.916079783}
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