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Simplifying 4x2 + 5x + -168 = 0 Reorder the terms: -168 + 5x + 4x2 = 0 Solving -168 + 5x + 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'. -42 + 1.25x + x2 = 0 Move the constant term to the right: Add '42' to each side of the equation. -42 + 1.25x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + 1.25x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 1.25x + x2 = 0 + 42 1.25x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 1.25x + x2 = 42 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 42 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 42 + 0.390625 Combine like terms: 42 + 0.390625 = 42.390625 0.390625 + 1.25x + x2 = 42.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 42.390625 Calculate the square root of the right side: 6.510808322 Break this problem into two subproblems by setting (x + 0.625) equal to 6.510808322 and -6.510808322.Subproblem 1
x + 0.625 = 6.510808322 Simplifying x + 0.625 = 6.510808322 Reorder the terms: 0.625 + x = 6.510808322 Solving 0.625 + x = 6.510808322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 6.510808322 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 6.510808322 + -0.625 x = 6.510808322 + -0.625 Combine like terms: 6.510808322 + -0.625 = 5.885808322 x = 5.885808322 Simplifying x = 5.885808322Subproblem 2
x + 0.625 = -6.510808322 Simplifying x + 0.625 = -6.510808322 Reorder the terms: 0.625 + x = -6.510808322 Solving 0.625 + x = -6.510808322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -6.510808322 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -6.510808322 + -0.625 x = -6.510808322 + -0.625 Combine like terms: -6.510808322 + -0.625 = -7.135808322 x = -7.135808322 Simplifying x = -7.135808322Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.885808322, -7.135808322}
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