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Simplifying 4x2 + 24x + -50 = 0 Reorder the terms: -50 + 24x + 4x2 = 0 Solving -50 + 24x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + 12x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + 12x + 2x2)' equal to zero and attempt to solve: Simplifying -25 + 12x + 2x2 = 0 Solving -25 + 12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + 6x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 6x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 6x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 6x + x2 = 0 + 12.5 6x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 6x + x2 = 12.5 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 12.5 + 9 Reorder the terms: 9 + 6x + x2 = 12.5 + 9 Combine like terms: 12.5 + 9 = 21.5 9 + 6x + x2 = 21.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 21.5 Calculate the square root of the right side: 4.636809248 Break this problem into two subproblems by setting (x + 3) equal to 4.636809248 and -4.636809248.Subproblem 1
x + 3 = 4.636809248 Simplifying x + 3 = 4.636809248 Reorder the terms: 3 + x = 4.636809248 Solving 3 + x = 4.636809248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 4.636809248 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.636809248 + -3 x = 4.636809248 + -3 Combine like terms: 4.636809248 + -3 = 1.636809248 x = 1.636809248 Simplifying x = 1.636809248Subproblem 2
x + 3 = -4.636809248 Simplifying x + 3 = -4.636809248 Reorder the terms: 3 + x = -4.636809248 Solving 3 + x = -4.636809248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -4.636809248 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.636809248 + -3 x = -4.636809248 + -3 Combine like terms: -4.636809248 + -3 = -7.636809248 x = -7.636809248 Simplifying x = -7.636809248Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.636809248, -7.636809248}Solution
x = {1.636809248, -7.636809248}
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