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Simplifying 5x(3x + -4) + -1(6 + 2) = x Reorder the terms: 5x(-4 + 3x) + -1(6 + 2) = x (-4 * 5x + 3x * 5x) + -1(6 + 2) = x (-20x + 15x2) + -1(6 + 2) = x Combine like terms: 6 + 2 = 8 -20x + 15x2 + -1(8) = x Multiply -1 * 8 -20x + 15x2 + -8 = x Reorder the terms: -8 + -20x + 15x2 = x Solving -8 + -20x + 15x2 = x Solving for variable 'x'. Reorder the terms: -8 + -20x + -1x + 15x2 = x + -1x Combine like terms: -20x + -1x = -21x -8 + -21x + 15x2 = x + -1x Combine like terms: x + -1x = 0 -8 + -21x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.5333333333 + -1.4x + x2 = 0 Move the constant term to the right: Add '0.5333333333' to each side of the equation. -0.5333333333 + -1.4x + 0.5333333333 + x2 = 0 + 0.5333333333 Reorder the terms: -0.5333333333 + 0.5333333333 + -1.4x + x2 = 0 + 0.5333333333 Combine like terms: -0.5333333333 + 0.5333333333 = 0.0000000000 0.0000000000 + -1.4x + x2 = 0 + 0.5333333333 -1.4x + x2 = 0 + 0.5333333333 Combine like terms: 0 + 0.5333333333 = 0.5333333333 -1.4x + x2 = 0.5333333333 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 0.5333333333 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 0.5333333333 + 0.49 Combine like terms: 0.5333333333 + 0.49 = 1.0233333333 0.49 + -1.4x + x2 = 1.0233333333 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 1.0233333333 Calculate the square root of the right side: 1.011599394 Break this problem into two subproblems by setting (x + -0.7) equal to 1.011599394 and -1.011599394.Subproblem 1
x + -0.7 = 1.011599394 Simplifying x + -0.7 = 1.011599394 Reorder the terms: -0.7 + x = 1.011599394 Solving -0.7 + x = 1.011599394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 1.011599394 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 1.011599394 + 0.7 x = 1.011599394 + 0.7 Combine like terms: 1.011599394 + 0.7 = 1.711599394 x = 1.711599394 Simplifying x = 1.711599394Subproblem 2
x + -0.7 = -1.011599394 Simplifying x + -0.7 = -1.011599394 Reorder the terms: -0.7 + x = -1.011599394 Solving -0.7 + x = -1.011599394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -1.011599394 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -1.011599394 + 0.7 x = -1.011599394 + 0.7 Combine like terms: -1.011599394 + 0.7 = -0.311599394 x = -0.311599394 Simplifying x = -0.311599394Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.711599394, -0.311599394}
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