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Simplifying 3x + -4x2 + 7 + 2x2 + -3 + 5x = 0 Reorder the terms: 7 + -3 + 3x + 5x + -4x2 + 2x2 = 0 Combine like terms: 7 + -3 = 4 4 + 3x + 5x + -4x2 + 2x2 = 0 Combine like terms: 3x + 5x = 8x 4 + 8x + -4x2 + 2x2 = 0 Combine like terms: -4x2 + 2x2 = -2x2 4 + 8x + -2x2 = 0 Solving 4 + 8x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 4x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying 2 + 4x + -1x2 = 0 Solving 2 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -4x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -4x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -4x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4x + x2 = 0 + 2 -4x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -4x + x2 = 2 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 = 2 + 4 Reorder the terms: 4 + -4x + x2 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + -4x + x2 = 6 Factor a perfect square on the left side: (x + -2)(x + -2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -2) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -2 = 2.449489743 Simplifying x + -2 = 2.449489743 Reorder the terms: -2 + x = 2.449489743 Solving -2 + x = 2.449489743 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 = 2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.449489743 + 2 x = 2.449489743 + 2 Combine like terms: 2.449489743 + 2 = 4.449489743 x = 4.449489743 Simplifying x = 4.449489743Subproblem 2
x + -2 = -2.449489743 Simplifying x + -2 = -2.449489743 Reorder the terms: -2 + x = -2.449489743 Solving -2 + x = -2.449489743 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 = -2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.449489743 + 2 x = -2.449489743 + 2 Combine like terms: -2.449489743 + 2 = -0.449489743 x = -0.449489743 Simplifying x = -0.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.449489743, -0.449489743}Solution
x = {4.449489743, -0.449489743}
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