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Simplifying 10x2 + -28x + -140 = 0 Reorder the terms: -140 + -28x + 10x2 = 0 Solving -140 + -28x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-70 + -14x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-70 + -14x + 5x2)' equal to zero and attempt to solve: Simplifying -70 + -14x + 5x2 = 0 Solving -70 + -14x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -14 + -2.8x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -2.8x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -2.8x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -2.8x + x2 = 0 + 14 -2.8x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -2.8x + x2 = 14 The x term is -2.8x. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8x + 1.96 + x2 = 14 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = 14 + 1.96 Combine like terms: 14 + 1.96 = 15.96 1.96 + -2.8x + x2 = 15.96 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 15.96 Calculate the square root of the right side: 3.994996871 Break this problem into two subproblems by setting (x + -1.4) equal to 3.994996871 and -3.994996871.Subproblem 1
x + -1.4 = 3.994996871 Simplifying x + -1.4 = 3.994996871 Reorder the terms: -1.4 + x = 3.994996871 Solving -1.4 + x = 3.994996871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 3.994996871 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 3.994996871 + 1.4 x = 3.994996871 + 1.4 Combine like terms: 3.994996871 + 1.4 = 5.394996871 x = 5.394996871 Simplifying x = 5.394996871Subproblem 2
x + -1.4 = -3.994996871 Simplifying x + -1.4 = -3.994996871 Reorder the terms: -1.4 + x = -3.994996871 Solving -1.4 + x = -3.994996871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -3.994996871 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -3.994996871 + 1.4 x = -3.994996871 + 1.4 Combine like terms: -3.994996871 + 1.4 = -2.594996871 x = -2.594996871 Simplifying x = -2.594996871Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.394996871, -2.594996871}Solution
x = {5.394996871, -2.594996871}
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