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Simplifying 5x(x + 4) = 3x + 23 Reorder the terms: 5x(4 + x) = 3x + 23 (4 * 5x + x * 5x) = 3x + 23 (20x + 5x2) = 3x + 23 Reorder the terms: 20x + 5x2 = 23 + 3x Solving 20x + 5x2 = 23 + 3x Solving for variable 'x'. Reorder the terms: -23 + 20x + -3x + 5x2 = 23 + 3x + -23 + -3x Combine like terms: 20x + -3x = 17x -23 + 17x + 5x2 = 23 + 3x + -23 + -3x Reorder the terms: -23 + 17x + 5x2 = 23 + -23 + 3x + -3x Combine like terms: 23 + -23 = 0 -23 + 17x + 5x2 = 0 + 3x + -3x -23 + 17x + 5x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -23 + 17x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.6 + 3.4x + x2 = 0 Move the constant term to the right: Add '4.6' to each side of the equation. -4.6 + 3.4x + 4.6 + x2 = 0 + 4.6 Reorder the terms: -4.6 + 4.6 + 3.4x + x2 = 0 + 4.6 Combine like terms: -4.6 + 4.6 = 0.0 0.0 + 3.4x + x2 = 0 + 4.6 3.4x + x2 = 0 + 4.6 Combine like terms: 0 + 4.6 = 4.6 3.4x + x2 = 4.6 The x term is 3.4x. Take half its coefficient (1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. 3.4x + 2.89 + x2 = 4.6 + 2.89 Reorder the terms: 2.89 + 3.4x + x2 = 4.6 + 2.89 Combine like terms: 4.6 + 2.89 = 7.49 2.89 + 3.4x + x2 = 7.49 Factor a perfect square on the left side: (x + 1.7)(x + 1.7) = 7.49 Calculate the square root of the right side: 2.736786437 Break this problem into two subproblems by setting (x + 1.7) equal to 2.736786437 and -2.736786437.Subproblem 1
x + 1.7 = 2.736786437 Simplifying x + 1.7 = 2.736786437 Reorder the terms: 1.7 + x = 2.736786437 Solving 1.7 + x = 2.736786437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = 2.736786437 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = 2.736786437 + -1.7 x = 2.736786437 + -1.7 Combine like terms: 2.736786437 + -1.7 = 1.036786437 x = 1.036786437 Simplifying x = 1.036786437Subproblem 2
x + 1.7 = -2.736786437 Simplifying x + 1.7 = -2.736786437 Reorder the terms: 1.7 + x = -2.736786437 Solving 1.7 + x = -2.736786437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = -2.736786437 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = -2.736786437 + -1.7 x = -2.736786437 + -1.7 Combine like terms: -2.736786437 + -1.7 = -4.436786437 x = -4.436786437 Simplifying x = -4.436786437Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.036786437, -4.436786437}
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