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Simplifying 9 + -2(4x + 5) * x = -4 Reorder the terms: 9 + -2(5 + 4x) * x = -4 Reorder the terms for easier multiplication: 9 + -2x(5 + 4x) = -4 9 + (5 * -2x + 4x * -2x) = -4 9 + (-10x + -8x2) = -4 Solving 9 + -10x + -8x2 = -4 Solving for variable 'x'. Reorder the terms: 9 + 4 + -10x + -8x2 = -4 + 4 Combine like terms: 9 + 4 = 13 13 + -10x + -8x2 = -4 + 4 Combine like terms: -4 + 4 = 0 13 + -10x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.625 + 1.25x + x2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + 1.25x + 1.625 + x2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + 1.25x + x2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + 1.25x + x2 = 0 + 1.625 1.25x + x2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 1.25x + x2 = 1.625 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 = 1.625 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 1.625 + 0.390625 Combine like terms: 1.625 + 0.390625 = 2.015625 0.390625 + 1.25x + x2 = 2.015625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 2.015625 Calculate the square root of the right side: 1.419727086 Break this problem into two subproblems by setting (x + 0.625) equal to 1.419727086 and -1.419727086.Subproblem 1
x + 0.625 = 1.419727086 Simplifying x + 0.625 = 1.419727086 Reorder the terms: 0.625 + x = 1.419727086 Solving 0.625 + x = 1.419727086 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 = 1.419727086 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 1.419727086 + -0.625 x = 1.419727086 + -0.625 Combine like terms: 1.419727086 + -0.625 = 0.794727086 x = 0.794727086 Simplifying x = 0.794727086Subproblem 2
x + 0.625 = -1.419727086 Simplifying x + 0.625 = -1.419727086 Reorder the terms: 0.625 + x = -1.419727086 Solving 0.625 + x = -1.419727086 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 = -1.419727086 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -1.419727086 + -0.625 x = -1.419727086 + -0.625 Combine like terms: -1.419727086 + -0.625 = -2.044727086 x = -2.044727086 Simplifying x = -2.044727086Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.794727086, -2.044727086}
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