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Simplifying 4x2 + 8x = 50 Reorder the terms: 8x + 4x2 = 50 Solving 8x + 4x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 8x + 4x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 8x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + 4x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + 4x + 2x2)' equal to zero and attempt to solve: Simplifying -25 + 4x + 2x2 = 0 Solving -25 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + 2x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 2x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 2x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 2x + x2 = 0 + 12.5 2x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 2x + x2 = 12.5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 12.5 + 1 Reorder the terms: 1 + 2x + x2 = 12.5 + 1 Combine like terms: 12.5 + 1 = 13.5 1 + 2x + x2 = 13.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 13.5 Calculate the square root of the right side: 3.674234614 Break this problem into two subproblems by setting (x + 1) equal to 3.674234614 and -3.674234614.Subproblem 1
x + 1 = 3.674234614 Simplifying x + 1 = 3.674234614 Reorder the terms: 1 + x = 3.674234614 Solving 1 + x = 3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.674234614 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.674234614 + -1 x = 3.674234614 + -1 Combine like terms: 3.674234614 + -1 = 2.674234614 x = 2.674234614 Simplifying x = 2.674234614Subproblem 2
x + 1 = -3.674234614 Simplifying x + 1 = -3.674234614 Reorder the terms: 1 + x = -3.674234614 Solving 1 + x = -3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.674234614 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.674234614 + -1 x = -3.674234614 + -1 Combine like terms: -3.674234614 + -1 = -4.674234614 x = -4.674234614 Simplifying x = -4.674234614Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.674234614, -4.674234614}Solution
x = {2.674234614, -4.674234614}
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