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Simplifying 2x2 + -32x + 94 = 0 Reorder the terms: 94 + -32x + 2x2 = 0 Solving 94 + -32x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(47 + -16x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(47 + -16x + x2)' equal to zero and attempt to solve: Simplifying 47 + -16x + x2 = 0 Solving 47 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-47' to each side of the equation. 47 + -16x + -47 + x2 = 0 + -47 Reorder the terms: 47 + -47 + -16x + x2 = 0 + -47 Combine like terms: 47 + -47 = 0 0 + -16x + x2 = 0 + -47 -16x + x2 = 0 + -47 Combine like terms: 0 + -47 = -47 -16x + x2 = -47 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -47 + 64 Reorder the terms: 64 + -16x + x2 = -47 + 64 Combine like terms: -47 + 64 = 17 64 + -16x + x2 = 17 Factor a perfect square on the left side: (x + -8)(x + -8) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + -8) equal to 4.123105626 and -4.123105626.Subproblem 1
x + -8 = 4.123105626 Simplifying x + -8 = 4.123105626 Reorder the terms: -8 + x = 4.123105626 Solving -8 + x = 4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 4.123105626 + 8 Combine like terms: -8 + 8 = 0 0 + x = 4.123105626 + 8 x = 4.123105626 + 8 Combine like terms: 4.123105626 + 8 = 12.123105626 x = 12.123105626 Simplifying x = 12.123105626Subproblem 2
x + -8 = -4.123105626 Simplifying x + -8 = -4.123105626 Reorder the terms: -8 + x = -4.123105626 Solving -8 + x = -4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -4.123105626 + 8 Combine like terms: -8 + 8 = 0 0 + x = -4.123105626 + 8 x = -4.123105626 + 8 Combine like terms: -4.123105626 + 8 = 3.876894374 x = 3.876894374 Simplifying x = 3.876894374Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.123105626, 3.876894374}Solution
x = {12.123105626, 3.876894374}
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