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Simplifying 4x2 + 5(x + -4) = 4 Reorder the terms: 4x2 + 5(-4 + x) = 4 4x2 + (-4 * 5 + x * 5) = 4 4x2 + (-20 + 5x) = 4 Reorder the terms: -20 + 5x + 4x2 = 4 Solving -20 + 5x + 4x2 = 4 Solving for variable 'x'. Reorder the terms: -20 + -4 + 5x + 4x2 = 4 + -4 Combine like terms: -20 + -4 = -24 -24 + 5x + 4x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -24 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6 + 1.25x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 1.25x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 1.25x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 1.25x + x2 = 0 + 6 1.25x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 1.25x + x2 = 6 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 = 6 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 6 + 0.390625 Combine like terms: 6 + 0.390625 = 6.390625 0.390625 + 1.25x + x2 = 6.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 6.390625 Calculate the square root of the right side: 2.527968552 Break this problem into two subproblems by setting (x + 0.625) equal to 2.527968552 and -2.527968552.Subproblem 1
x + 0.625 = 2.527968552 Simplifying x + 0.625 = 2.527968552 Reorder the terms: 0.625 + x = 2.527968552 Solving 0.625 + x = 2.527968552 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 = 2.527968552 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 2.527968552 + -0.625 x = 2.527968552 + -0.625 Combine like terms: 2.527968552 + -0.625 = 1.902968552 x = 1.902968552 Simplifying x = 1.902968552Subproblem 2
x + 0.625 = -2.527968552 Simplifying x + 0.625 = -2.527968552 Reorder the terms: 0.625 + x = -2.527968552 Solving 0.625 + x = -2.527968552 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 = -2.527968552 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -2.527968552 + -0.625 x = -2.527968552 + -0.625 Combine like terms: -2.527968552 + -0.625 = -3.152968552 x = -3.152968552 Simplifying x = -3.152968552Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.902968552, -3.152968552}
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