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Simplifying 6x2 + -48x + 96 = 300 Reorder the terms: 96 + -48x + 6x2 = 300 Solving 96 + -48x + 6x2 = 300 Solving for variable 'x'. Reorder the terms: 96 + -300 + -48x + 6x2 = 300 + -300 Combine like terms: 96 + -300 = -204 -204 + -48x + 6x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -204 + -48x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-34 + -8x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-34 + -8x + x2)' equal to zero and attempt to solve: Simplifying -34 + -8x + x2 = 0 Solving -34 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + -8x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + -8x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + -8x + x2 = 0 + 34 -8x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 -8x + x2 = 34 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 34 + 16 Reorder the terms: 16 + -8x + x2 = 34 + 16 Combine like terms: 34 + 16 = 50 16 + -8x + x2 = 50 Factor a perfect square on the left side: (x + -4)(x + -4) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + -4) equal to 7.071067812 and -7.071067812.Subproblem 1
x + -4 = 7.071067812 Simplifying x + -4 = 7.071067812 Reorder the terms: -4 + x = 7.071067812 Solving -4 + x = 7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 7.071067812 + 4 Combine like terms: -4 + 4 = 0 0 + x = 7.071067812 + 4 x = 7.071067812 + 4 Combine like terms: 7.071067812 + 4 = 11.071067812 x = 11.071067812 Simplifying x = 11.071067812Subproblem 2
x + -4 = -7.071067812 Simplifying x + -4 = -7.071067812 Reorder the terms: -4 + x = -7.071067812 Solving -4 + x = -7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -7.071067812 + 4 Combine like terms: -4 + 4 = 0 0 + x = -7.071067812 + 4 x = -7.071067812 + 4 Combine like terms: -7.071067812 + 4 = -3.071067812 x = -3.071067812 Simplifying x = -3.071067812Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.071067812, -3.071067812}Solution
x = {11.071067812, -3.071067812}
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