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Simplifying 4x2 + 48x + -28 = 0 Reorder the terms: -28 + 48x + 4x2 = 0 Solving -28 + 48x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-7 + 12x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + 12x + x2)' equal to zero and attempt to solve: Simplifying -7 + 12x + x2 = 0 Solving -7 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 12x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 12x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 12x + x2 = 0 + 7 12x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 12x + x2 = 7 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 = 7 + 36 Reorder the terms: 36 + 12x + x2 = 7 + 36 Combine like terms: 7 + 36 = 43 36 + 12x + x2 = 43 Factor a perfect square on the left side: (x + 6)(x + 6) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (x + 6) equal to 6.557438524 and -6.557438524.Subproblem 1
x + 6 = 6.557438524 Simplifying x + 6 = 6.557438524 Reorder the terms: 6 + x = 6.557438524 Solving 6 + x = 6.557438524 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 = 6.557438524 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.557438524 + -6 x = 6.557438524 + -6 Combine like terms: 6.557438524 + -6 = 0.557438524 x = 0.557438524 Simplifying x = 0.557438524Subproblem 2
x + 6 = -6.557438524 Simplifying x + 6 = -6.557438524 Reorder the terms: 6 + x = -6.557438524 Solving 6 + x = -6.557438524 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 = -6.557438524 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.557438524 + -6 x = -6.557438524 + -6 Combine like terms: -6.557438524 + -6 = -12.557438524 x = -12.557438524 Simplifying x = -12.557438524Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.557438524, -12.557438524}Solution
x = {0.557438524, -12.557438524}
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