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Simplifying 5(x2 + -4x) + -1(x + 1) = 0 Reorder the terms: 5(-4x + x2) + -1(x + 1) = 0 (-4x * 5 + x2 * 5) + -1(x + 1) = 0 (-20x + 5x2) + -1(x + 1) = 0 Reorder the terms: -20x + 5x2 + -1(1 + x) = 0 -20x + 5x2 + (1 * -1 + x * -1) = 0 -20x + 5x2 + (-1 + -1x) = 0 Reorder the terms: -1 + -20x + -1x + 5x2 = 0 Combine like terms: -20x + -1x = -21x -1 + -21x + 5x2 = 0 Solving -1 + -21x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -4.2x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -4.2x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -4.2x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -4.2x + x2 = 0 + 0.2 -4.2x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -4.2x + x2 = 0.2 The x term is -4.2x. Take half its coefficient (-2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. -4.2x + 4.41 + x2 = 0.2 + 4.41 Reorder the terms: 4.41 + -4.2x + x2 = 0.2 + 4.41 Combine like terms: 0.2 + 4.41 = 4.61 4.41 + -4.2x + x2 = 4.61 Factor a perfect square on the left side: (x + -2.1)(x + -2.1) = 4.61 Calculate the square root of the right side: 2.147091055 Break this problem into two subproblems by setting (x + -2.1) equal to 2.147091055 and -2.147091055.Subproblem 1
x + -2.1 = 2.147091055 Simplifying x + -2.1 = 2.147091055 Reorder the terms: -2.1 + x = 2.147091055 Solving -2.1 + x = 2.147091055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + x = 2.147091055 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + x = 2.147091055 + 2.1 x = 2.147091055 + 2.1 Combine like terms: 2.147091055 + 2.1 = 4.247091055 x = 4.247091055 Simplifying x = 4.247091055Subproblem 2
x + -2.1 = -2.147091055 Simplifying x + -2.1 = -2.147091055 Reorder the terms: -2.1 + x = -2.147091055 Solving -2.1 + x = -2.147091055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + x = -2.147091055 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + x = -2.147091055 + 2.1 x = -2.147091055 + 2.1 Combine like terms: -2.147091055 + 2.1 = -0.047091055 x = -0.047091055 Simplifying x = -0.047091055Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.247091055, -0.047091055}
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