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Simplifying -1(x + -2.1)(5x + -7.5) = 0 Reorder the terms: -1(-2.1 + x)(5x + -7.5) = 0 Reorder the terms: -1(-2.1 + x)(-7.5 + 5x) = 0 Multiply (-2.1 + x) * (-7.5 + 5x) -1(-2.1(-7.5 + 5x) + x(-7.5 + 5x)) = 0 -1((-7.5 * -2.1 + 5x * -2.1) + x(-7.5 + 5x)) = 0 -1((15.75 + -10.5x) + x(-7.5 + 5x)) = 0 -1(15.75 + -10.5x + (-7.5 * x + 5x * x)) = 0 -1(15.75 + -10.5x + (-7.5x + 5x2)) = 0 Combine like terms: -10.5x + -7.5x = -18x -1(15.75 + -18x + 5x2) = 0 (15.75 * -1 + -18x * -1 + 5x2 * -1) = 0 (-15.75 + 18x + -5x2) = 0 Solving -15.75 + 18x + -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'. 3.15 + -3.6x + x2 = 0 Move the constant term to the right: Add '-3.15' to each side of the equation. 3.15 + -3.6x + -3.15 + x2 = 0 + -3.15 Reorder the terms: 3.15 + -3.15 + -3.6x + x2 = 0 + -3.15 Combine like terms: 3.15 + -3.15 = 0.00 0.00 + -3.6x + x2 = 0 + -3.15 -3.6x + x2 = 0 + -3.15 Combine like terms: 0 + -3.15 = -3.15 -3.6x + x2 = -3.15 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = -3.15 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = -3.15 + 3.24 Combine like terms: -3.15 + 3.24 = 0.09 3.24 + -3.6x + x2 = 0.09 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 0.09 Calculate the square root of the right side: 0.3 Break this problem into two subproblems by setting (x + -1.8) equal to 0.3 and -0.3.Subproblem 1
x + -1.8 = 0.3 Simplifying x + -1.8 = 0.3 Reorder the terms: -1.8 + x = 0.3 Solving -1.8 + x = 0.3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 0.3 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 0.3 + 1.8 x = 0.3 + 1.8 Combine like terms: 0.3 + 1.8 = 2.1 x = 2.1 Simplifying x = 2.1Subproblem 2
x + -1.8 = -0.3 Simplifying x + -1.8 = -0.3 Reorder the terms: -1.8 + x = -0.3 Solving -1.8 + x = -0.3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -0.3 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -0.3 + 1.8 x = -0.3 + 1.8 Combine like terms: -0.3 + 1.8 = 1.5 x = 1.5 Simplifying x = 1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1, 1.5}
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