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Simplifying 15 + 8x + -4x2 = 3 + -2x2 Solving 15 + 8x + -4x2 = 3 + -2x2 Solving for variable 'x'. Reorder the terms: 15 + -3 + 8x + -4x2 + 2x2 = 3 + -2x2 + -3 + 2x2 Combine like terms: 15 + -3 = 12 12 + 8x + -4x2 + 2x2 = 3 + -2x2 + -3 + 2x2 Combine like terms: -4x2 + 2x2 = -2x2 12 + 8x + -2x2 = 3 + -2x2 + -3 + 2x2 Reorder the terms: 12 + 8x + -2x2 = 3 + -3 + -2x2 + 2x2 Combine like terms: 3 + -3 = 0 12 + 8x + -2x2 = 0 + -2x2 + 2x2 12 + 8x + -2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 12 + 8x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 4x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying 6 + 4x + -1x2 = 0 Solving 6 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6 + -4x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -4x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -4x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -4x + x2 = 0 + 6 -4x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -4x + x2 = 6 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 6 + 4 Reorder the terms: 4 + -4x + x2 = 6 + 4 Combine like terms: 6 + 4 = 10 4 + -4x + x2 = 10 Factor a perfect square on the left side: (x + -2)(x + -2) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + -2) equal to 3.16227766 and -3.16227766.Subproblem 1
x + -2 = 3.16227766 Simplifying x + -2 = 3.16227766 Reorder the terms: -2 + x = 3.16227766 Solving -2 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.16227766 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.16227766 + 2 x = 3.16227766 + 2 Combine like terms: 3.16227766 + 2 = 5.16227766 x = 5.16227766 Simplifying x = 5.16227766Subproblem 2
x + -2 = -3.16227766 Simplifying x + -2 = -3.16227766 Reorder the terms: -2 + x = -3.16227766 Solving -2 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.16227766 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.16227766 + 2 x = -3.16227766 + 2 Combine like terms: -3.16227766 + 2 = -1.16227766 x = -1.16227766 Simplifying x = -1.16227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.16227766, -1.16227766}Solution
x = {5.16227766, -1.16227766}
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