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Simplifying 4(x2 + 24x + -78) = 0 Reorder the terms: 4(-78 + 24x + x2) = 0 (-78 * 4 + 24x * 4 + x2 * 4) = 0 (-312 + 96x + 4x2) = 0 Solving -312 + 96x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-78 + 24x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-78 + 24x + x2)' equal to zero and attempt to solve: Simplifying -78 + 24x + x2 = 0 Solving -78 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '78' to each side of the equation. -78 + 24x + 78 + x2 = 0 + 78 Reorder the terms: -78 + 78 + 24x + x2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + 24x + x2 = 0 + 78 24x + x2 = 0 + 78 Combine like terms: 0 + 78 = 78 24x + x2 = 78 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 78 + 144 Reorder the terms: 144 + 24x + x2 = 78 + 144 Combine like terms: 78 + 144 = 222 144 + 24x + x2 = 222 Factor a perfect square on the left side: (x + 12)(x + 12) = 222 Calculate the square root of the right side: 14.899664426 Break this problem into two subproblems by setting (x + 12) equal to 14.899664426 and -14.899664426.Subproblem 1
x + 12 = 14.899664426 Simplifying x + 12 = 14.899664426 Reorder the terms: 12 + x = 14.899664426 Solving 12 + x = 14.899664426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 14.899664426 + -12 Combine like terms: 12 + -12 = 0 0 + x = 14.899664426 + -12 x = 14.899664426 + -12 Combine like terms: 14.899664426 + -12 = 2.899664426 x = 2.899664426 Simplifying x = 2.899664426Subproblem 2
x + 12 = -14.899664426 Simplifying x + 12 = -14.899664426 Reorder the terms: 12 + x = -14.899664426 Solving 12 + x = -14.899664426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -14.899664426 + -12 Combine like terms: 12 + -12 = 0 0 + x = -14.899664426 + -12 x = -14.899664426 + -12 Combine like terms: -14.899664426 + -12 = -26.899664426 x = -26.899664426 Simplifying x = -26.899664426Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.899664426, -26.899664426}Solution
x = {2.899664426, -26.899664426}
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