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Simplifying 5x(x + -1) + -4(x + 4) = 5 Reorder the terms: 5x(-1 + x) + -4(x + 4) = 5 (-1 * 5x + x * 5x) + -4(x + 4) = 5 (-5x + 5x2) + -4(x + 4) = 5 Reorder the terms: -5x + 5x2 + -4(4 + x) = 5 -5x + 5x2 + (4 * -4 + x * -4) = 5 -5x + 5x2 + (-16 + -4x) = 5 Reorder the terms: -16 + -5x + -4x + 5x2 = 5 Combine like terms: -5x + -4x = -9x -16 + -9x + 5x2 = 5 Solving -16 + -9x + 5x2 = 5 Solving for variable 'x'. Reorder the terms: -16 + -5 + -9x + 5x2 = 5 + -5 Combine like terms: -16 + -5 = -21 -21 + -9x + 5x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -21 + -9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.2 + -1.8x + x2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + -1.8x + 4.2 + x2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + -1.8x + x2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + -1.8x + x2 = 0 + 4.2 -1.8x + x2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 -1.8x + x2 = 4.2 The x term is -1.8x. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x + 0.81 + x2 = 4.2 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 4.2 + 0.81 Combine like terms: 4.2 + 0.81 = 5.01 0.81 + -1.8x + x2 = 5.01 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 5.01 Calculate the square root of the right side: 2.238302929 Break this problem into two subproblems by setting (x + -0.9) equal to 2.238302929 and -2.238302929.Subproblem 1
x + -0.9 = 2.238302929 Simplifying x + -0.9 = 2.238302929 Reorder the terms: -0.9 + x = 2.238302929 Solving -0.9 + x = 2.238302929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 2.238302929 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 2.238302929 + 0.9 x = 2.238302929 + 0.9 Combine like terms: 2.238302929 + 0.9 = 3.138302929 x = 3.138302929 Simplifying x = 3.138302929Subproblem 2
x + -0.9 = -2.238302929 Simplifying x + -0.9 = -2.238302929 Reorder the terms: -0.9 + x = -2.238302929 Solving -0.9 + x = -2.238302929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = -2.238302929 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -2.238302929 + 0.9 x = -2.238302929 + 0.9 Combine like terms: -2.238302929 + 0.9 = -1.338302929 x = -1.338302929 Simplifying x = -1.338302929Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.138302929, -1.338302929}
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