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Simplifying x2 + 14x = -1x2 + -10x + 150 Reorder the terms: 14x + x2 = -1x2 + -10x + 150 Reorder the terms: 14x + x2 = 150 + -10x + -1x2 Solving 14x + x2 = 150 + -10x + -1x2 Solving for variable 'x'. Reorder the terms: -150 + 14x + 10x + x2 + x2 = 150 + -10x + -1x2 + -150 + 10x + x2 Combine like terms: 14x + 10x = 24x -150 + 24x + x2 + x2 = 150 + -10x + -1x2 + -150 + 10x + x2 Combine like terms: x2 + x2 = 2x2 -150 + 24x + 2x2 = 150 + -10x + -1x2 + -150 + 10x + x2 Reorder the terms: -150 + 24x + 2x2 = 150 + -150 + -10x + 10x + -1x2 + x2 Combine like terms: 150 + -150 = 0 -150 + 24x + 2x2 = 0 + -10x + 10x + -1x2 + x2 -150 + 24x + 2x2 = -10x + 10x + -1x2 + x2 Combine like terms: -10x + 10x = 0 -150 + 24x + 2x2 = 0 + -1x2 + x2 -150 + 24x + 2x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -150 + 24x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-75 + 12x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-75 + 12x + x2)' equal to zero and attempt to solve: Simplifying -75 + 12x + x2 = 0 Solving -75 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + 12x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 12x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 12x + x2 = 0 + 75 12x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 12x + x2 = 75 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 75 + 36 Reorder the terms: 36 + 12x + x2 = 75 + 36 Combine like terms: 75 + 36 = 111 36 + 12x + x2 = 111 Factor a perfect square on the left side: (x + 6)(x + 6) = 111 Calculate the square root of the right side: 10.535653753 Break this problem into two subproblems by setting (x + 6) equal to 10.535653753 and -10.535653753.Subproblem 1
x + 6 = 10.535653753 Simplifying x + 6 = 10.535653753 Reorder the terms: 6 + x = 10.535653753 Solving 6 + x = 10.535653753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 10.535653753 + -6 Combine like terms: 6 + -6 = 0 0 + x = 10.535653753 + -6 x = 10.535653753 + -6 Combine like terms: 10.535653753 + -6 = 4.535653753 x = 4.535653753 Simplifying x = 4.535653753Subproblem 2
x + 6 = -10.535653753 Simplifying x + 6 = -10.535653753 Reorder the terms: 6 + x = -10.535653753 Solving 6 + x = -10.535653753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -10.535653753 + -6 Combine like terms: 6 + -6 = 0 0 + x = -10.535653753 + -6 x = -10.535653753 + -6 Combine like terms: -10.535653753 + -6 = -16.535653753 x = -16.535653753 Simplifying x = -16.535653753Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.535653753, -16.535653753}Solution
x = {4.535653753, -16.535653753}
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