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Simplifying 4(3x + x) + 7 + -5x = 8 + (5x)(5x + -6x) + 23 Combine like terms: 3x + x = 4x 4(4x) + 7 + -5x = 8 + (5x)(5x + -6x) + 23 Remove parenthesis around (4x) 4 * 4x + 7 + -5x = 8 + (5x)(5x + -6x) + 23 Multiply 4 * 4 16x + 7 + -5x = 8 + (5x)(5x + -6x) + 23 Reorder the terms: 7 + 16x + -5x = 8 + (5x)(5x + -6x) + 23 Combine like terms: 16x + -5x = 11x 7 + 11x = 8 + (5x)(5x + -6x) + 23 Remove parenthesis around (5x) 7 + 11x = 8 + 5x(5x + -6x) + 23 Combine like terms: 5x + -6x = -1x 7 + 11x = 8 + 5x(-1x) + 23 Remove parenthesis around (-1x) 7 + 11x = 8 + 5x * -1x + 23 Reorder the terms for easier multiplication: 7 + 11x = 8 + 5 * -1x * x + 23 Multiply 5 * -1 7 + 11x = 8 + -5x * x + 23 Multiply x * x 7 + 11x = 8 + -5x2 + 23 Reorder the terms: 7 + 11x = 8 + 23 + -5x2 Combine like terms: 8 + 23 = 31 7 + 11x = 31 + -5x2 Solving 7 + 11x = 31 + -5x2 Solving for variable 'x'. Reorder the terms: 7 + -31 + 11x + 5x2 = 31 + -5x2 + -31 + 5x2 Combine like terms: 7 + -31 = -24 -24 + 11x + 5x2 = 31 + -5x2 + -31 + 5x2 Reorder the terms: -24 + 11x + 5x2 = 31 + -31 + -5x2 + 5x2 Combine like terms: 31 + -31 = 0 -24 + 11x + 5x2 = 0 + -5x2 + 5x2 -24 + 11x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -24 + 11x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.8 + 2.2x + x2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + 2.2x + 4.8 + x2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + 2.2x + x2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + 2.2x + x2 = 0 + 4.8 2.2x + x2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 2.2x + x2 = 4.8 The x term is 2.2x. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2x + 1.21 + x2 = 4.8 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = 4.8 + 1.21 Combine like terms: 4.8 + 1.21 = 6.01 1.21 + 2.2x + x2 = 6.01 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 6.01 Calculate the square root of the right side: 2.451530134 Break this problem into two subproblems by setting (x + 1.1) equal to 2.451530134 and -2.451530134.Subproblem 1
x + 1.1 = 2.451530134 Simplifying x + 1.1 = 2.451530134 Reorder the terms: 1.1 + x = 2.451530134 Solving 1.1 + x = 2.451530134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = 2.451530134 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 2.451530134 + -1.1 x = 2.451530134 + -1.1 Combine like terms: 2.451530134 + -1.1 = 1.351530134 x = 1.351530134 Simplifying x = 1.351530134Subproblem 2
x + 1.1 = -2.451530134 Simplifying x + 1.1 = -2.451530134 Reorder the terms: 1.1 + x = -2.451530134 Solving 1.1 + x = -2.451530134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = -2.451530134 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -2.451530134 + -1.1 x = -2.451530134 + -1.1 Combine like terms: -2.451530134 + -1.1 = -3.551530134 x = -3.551530134 Simplifying x = -3.551530134Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.351530134, -3.551530134}
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