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Simplifying 4x2 + 26x + -15 = 0 Reorder the terms: -15 + 26x + 4x2 = 0 Solving -15 + 26x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + 6.5x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 6.5x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 6.5x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 6.5x + x2 = 0 + 3.75 6.5x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 6.5x + x2 = 3.75 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = 3.75 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 3.75 + 10.5625 Combine like terms: 3.75 + 10.5625 = 14.3125 10.5625 + 6.5x + x2 = 14.3125 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 14.3125 Calculate the square root of the right side: 3.783186488 Break this problem into two subproblems by setting (x + 3.25) equal to 3.783186488 and -3.783186488.Subproblem 1
x + 3.25 = 3.783186488 Simplifying x + 3.25 = 3.783186488 Reorder the terms: 3.25 + x = 3.783186488 Solving 3.25 + x = 3.783186488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 3.783186488 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 3.783186488 + -3.25 x = 3.783186488 + -3.25 Combine like terms: 3.783186488 + -3.25 = 0.533186488 x = 0.533186488 Simplifying x = 0.533186488Subproblem 2
x + 3.25 = -3.783186488 Simplifying x + 3.25 = -3.783186488 Reorder the terms: 3.25 + x = -3.783186488 Solving 3.25 + x = -3.783186488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -3.783186488 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -3.783186488 + -3.25 x = -3.783186488 + -3.25 Combine like terms: -3.783186488 + -3.25 = -7.033186488 x = -7.033186488 Simplifying x = -7.033186488Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.533186488, -7.033186488}
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