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Simplifying 2x(5x + 4) + -7 = -3x + 2 Reorder the terms: 2x(4 + 5x) + -7 = -3x + 2 (4 * 2x + 5x * 2x) + -7 = -3x + 2 (8x + 10x2) + -7 = -3x + 2 Reorder the terms: -7 + 8x + 10x2 = -3x + 2 Reorder the terms: -7 + 8x + 10x2 = 2 + -3x Solving -7 + 8x + 10x2 = 2 + -3x Solving for variable 'x'. Reorder the terms: -7 + -2 + 8x + 3x + 10x2 = 2 + -3x + -2 + 3x Combine like terms: -7 + -2 = -9 -9 + 8x + 3x + 10x2 = 2 + -3x + -2 + 3x Combine like terms: 8x + 3x = 11x -9 + 11x + 10x2 = 2 + -3x + -2 + 3x Reorder the terms: -9 + 11x + 10x2 = 2 + -2 + -3x + 3x Combine like terms: 2 + -2 = 0 -9 + 11x + 10x2 = 0 + -3x + 3x -9 + 11x + 10x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -9 + 11x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.9 + 1.1x + x2 = 0.0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + 1.1x + 0.9 + x2 = 0.0 + 0.9 Reorder the terms: -0.9 + 0.9 + 1.1x + x2 = 0.0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + 1.1x + x2 = 0.0 + 0.9 1.1x + x2 = 0.0 + 0.9 Combine like terms: 0.0 + 0.9 = 0.9 1.1x + x2 = 0.9 The x term is 1.1x. Take half its coefficient (0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. 1.1x + 0.3025 + x2 = 0.9 + 0.3025 Reorder the terms: 0.3025 + 1.1x + x2 = 0.9 + 0.3025 Combine like terms: 0.9 + 0.3025 = 1.2025 0.3025 + 1.1x + x2 = 1.2025 Factor a perfect square on the left side: (x + 0.55)(x + 0.55) = 1.2025 Calculate the square root of the right side: 1.09658561 Break this problem into two subproblems by setting (x + 0.55) equal to 1.09658561 and -1.09658561.Subproblem 1
x + 0.55 = 1.09658561 Simplifying x + 0.55 = 1.09658561 Reorder the terms: 0.55 + x = 1.09658561 Solving 0.55 + x = 1.09658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.55' to each side of the equation. 0.55 + -0.55 + x = 1.09658561 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = 1.09658561 + -0.55 x = 1.09658561 + -0.55 Combine like terms: 1.09658561 + -0.55 = 0.54658561 x = 0.54658561 Simplifying x = 0.54658561Subproblem 2
x + 0.55 = -1.09658561 Simplifying x + 0.55 = -1.09658561 Reorder the terms: 0.55 + x = -1.09658561 Solving 0.55 + x = -1.09658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.55' to each side of the equation. 0.55 + -0.55 + x = -1.09658561 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = -1.09658561 + -0.55 x = -1.09658561 + -0.55 Combine like terms: -1.09658561 + -0.55 = -1.64658561 x = -1.64658561 Simplifying x = -1.64658561Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.54658561, -1.64658561}
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