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Simplifying 5x(2x + -3) = 8x + 3 Reorder the terms: 5x(-3 + 2x) = 8x + 3 (-3 * 5x + 2x * 5x) = 8x + 3 (-15x + 10x2) = 8x + 3 Reorder the terms: -15x + 10x2 = 3 + 8x Solving -15x + 10x2 = 3 + 8x Solving for variable 'x'. Reorder the terms: -3 + -15x + -8x + 10x2 = 3 + 8x + -3 + -8x Combine like terms: -15x + -8x = -23x -3 + -23x + 10x2 = 3 + 8x + -3 + -8x Reorder the terms: -3 + -23x + 10x2 = 3 + -3 + 8x + -8x Combine like terms: 3 + -3 = 0 -3 + -23x + 10x2 = 0 + 8x + -8x -3 + -23x + 10x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -3 + -23x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + -2.3x + x2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -2.3x + 0.3 + x2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + -2.3x + x2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -2.3x + x2 = 0.0 + 0.3 -2.3x + x2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 -2.3x + x2 = 0.3 The x term is -2.3x. Take half its coefficient (-1.15). Square it (1.3225) and add it to both sides. Add '1.3225' to each side of the equation. -2.3x + 1.3225 + x2 = 0.3 + 1.3225 Reorder the terms: 1.3225 + -2.3x + x2 = 0.3 + 1.3225 Combine like terms: 0.3 + 1.3225 = 1.6225 1.3225 + -2.3x + x2 = 1.6225 Factor a perfect square on the left side: (x + -1.15)(x + -1.15) = 1.6225 Calculate the square root of the right side: 1.27377392 Break this problem into two subproblems by setting (x + -1.15) equal to 1.27377392 and -1.27377392.Subproblem 1
x + -1.15 = 1.27377392 Simplifying x + -1.15 = 1.27377392 Reorder the terms: -1.15 + x = 1.27377392 Solving -1.15 + x = 1.27377392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + x = 1.27377392 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + x = 1.27377392 + 1.15 x = 1.27377392 + 1.15 Combine like terms: 1.27377392 + 1.15 = 2.42377392 x = 2.42377392 Simplifying x = 2.42377392Subproblem 2
x + -1.15 = -1.27377392 Simplifying x + -1.15 = -1.27377392 Reorder the terms: -1.15 + x = -1.27377392 Solving -1.15 + x = -1.27377392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + x = -1.27377392 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + x = -1.27377392 + 1.15 x = -1.27377392 + 1.15 Combine like terms: -1.27377392 + 1.15 = -0.12377392 x = -0.12377392 Simplifying x = -0.12377392Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.42377392, -0.12377392}
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