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Simplifying 4x2 + 8x + -59 = 0 Reorder the terms: -59 + 8x + 4x2 = 0 Solving -59 + 8x + 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'. -14.75 + 2x + x2 = 0 Move the constant term to the right: Add '14.75' to each side of the equation. -14.75 + 2x + 14.75 + x2 = 0 + 14.75 Reorder the terms: -14.75 + 14.75 + 2x + x2 = 0 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + 2x + x2 = 0 + 14.75 2x + x2 = 0 + 14.75 Combine like terms: 0 + 14.75 = 14.75 2x + x2 = 14.75 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 = 14.75 + 1 Reorder the terms: 1 + 2x + x2 = 14.75 + 1 Combine like terms: 14.75 + 1 = 15.75 1 + 2x + x2 = 15.75 Factor a perfect square on the left side: (x + 1)(x + 1) = 15.75 Calculate the square root of the right side: 3.968626967 Break this problem into two subproblems by setting (x + 1) equal to 3.968626967 and -3.968626967.Subproblem 1
x + 1 = 3.968626967 Simplifying x + 1 = 3.968626967 Reorder the terms: 1 + x = 3.968626967 Solving 1 + x = 3.968626967 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 = 3.968626967 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.968626967 + -1 x = 3.968626967 + -1 Combine like terms: 3.968626967 + -1 = 2.968626967 x = 2.968626967 Simplifying x = 2.968626967Subproblem 2
x + 1 = -3.968626967 Simplifying x + 1 = -3.968626967 Reorder the terms: 1 + x = -3.968626967 Solving 1 + x = -3.968626967 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 = -3.968626967 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.968626967 + -1 x = -3.968626967 + -1 Combine like terms: -3.968626967 + -1 = -4.968626967 x = -4.968626967 Simplifying x = -4.968626967Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.968626967, -4.968626967}
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