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Simplifying 2x(5x + -7) = 2x * 2 + -5 Reorder the terms: 2x(-7 + 5x) = 2x * 2 + -5 (-7 * 2x + 5x * 2x) = 2x * 2 + -5 (-14x + 10x2) = 2x * 2 + -5 Reorder the terms for easier multiplication: -14x + 10x2 = 2 * 2x + -5 Multiply 2 * 2 -14x + 10x2 = 4x + -5 Reorder the terms: -14x + 10x2 = -5 + 4x Solving -14x + 10x2 = -5 + 4x Solving for variable 'x'. Reorder the terms: 5 + -14x + -4x + 10x2 = -5 + 4x + 5 + -4x Combine like terms: -14x + -4x = -18x 5 + -18x + 10x2 = -5 + 4x + 5 + -4x Reorder the terms: 5 + -18x + 10x2 = -5 + 5 + 4x + -4x Combine like terms: -5 + 5 = 0 5 + -18x + 10x2 = 0 + 4x + -4x 5 + -18x + 10x2 = 4x + -4x Combine like terms: 4x + -4x = 0 5 + -18x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.5 + -1.8x + x2 = 0.0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.8x + -0.5 + x2 = 0.0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.8x + x2 = 0.0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.8x + x2 = 0.0 + -0.5 -1.8x + x2 = 0.0 + -0.5 Combine like terms: 0.0 + -0.5 = -0.5 -1.8x + x2 = -0.5 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 = -0.5 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = -0.5 + 0.81 Combine like terms: -0.5 + 0.81 = 0.31 0.81 + -1.8x + x2 = 0.31 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 0.31 Calculate the square root of the right side: 0.556776436 Break this problem into two subproblems by setting (x + -0.9) equal to 0.556776436 and -0.556776436.Subproblem 1
x + -0.9 = 0.556776436 Simplifying x + -0.9 = 0.556776436 Reorder the terms: -0.9 + x = 0.556776436 Solving -0.9 + x = 0.556776436 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 = 0.556776436 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 0.556776436 + 0.9 x = 0.556776436 + 0.9 Combine like terms: 0.556776436 + 0.9 = 1.456776436 x = 1.456776436 Simplifying x = 1.456776436Subproblem 2
x + -0.9 = -0.556776436 Simplifying x + -0.9 = -0.556776436 Reorder the terms: -0.9 + x = -0.556776436 Solving -0.9 + x = -0.556776436 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 = -0.556776436 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -0.556776436 + 0.9 x = -0.556776436 + 0.9 Combine like terms: -0.556776436 + 0.9 = 0.343223564 x = 0.343223564 Simplifying x = 0.343223564Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.456776436, 0.343223564}
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