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Simplifying 99 = 4x2 + -5x Reorder the terms: 99 = -5x + 4x2 Solving 99 = -5x + 4x2 Solving for variable 'x'. Reorder the terms: 99 + 5x + -4x2 = -5x + 5x + 4x2 + -4x2 Combine like terms: -5x + 5x = 0 99 + 5x + -4x2 = 0 + 4x2 + -4x2 99 + 5x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 99 + 5x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -24.75 + -1.25x + x2 = 0 Move the constant term to the right: Add '24.75' to each side of the equation. -24.75 + -1.25x + 24.75 + x2 = 0 + 24.75 Reorder the terms: -24.75 + 24.75 + -1.25x + x2 = 0 + 24.75 Combine like terms: -24.75 + 24.75 = 0.00 0.00 + -1.25x + x2 = 0 + 24.75 -1.25x + x2 = 0 + 24.75 Combine like terms: 0 + 24.75 = 24.75 -1.25x + x2 = 24.75 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 = 24.75 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 24.75 + 0.390625 Combine like terms: 24.75 + 0.390625 = 25.140625 0.390625 + -1.25x + x2 = 25.140625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 25.140625 Calculate the square root of the right side: 5.01404278 Break this problem into two subproblems by setting (x + -0.625) equal to 5.01404278 and -5.01404278.Subproblem 1
x + -0.625 = 5.01404278 Simplifying x + -0.625 = 5.01404278 Reorder the terms: -0.625 + x = 5.01404278 Solving -0.625 + x = 5.01404278 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 = 5.01404278 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 5.01404278 + 0.625 x = 5.01404278 + 0.625 Combine like terms: 5.01404278 + 0.625 = 5.63904278 x = 5.63904278 Simplifying x = 5.63904278Subproblem 2
x + -0.625 = -5.01404278 Simplifying x + -0.625 = -5.01404278 Reorder the terms: -0.625 + x = -5.01404278 Solving -0.625 + x = -5.01404278 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 = -5.01404278 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -5.01404278 + 0.625 x = -5.01404278 + 0.625 Combine like terms: -5.01404278 + 0.625 = -4.38904278 x = -4.38904278 Simplifying x = -4.38904278Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.63904278, -4.38904278}
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