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Simplifying 23x + -5x(2x) + 3 = 0 Remove parenthesis around (2x) 23x + -5x * 2x + 3 = 0 Reorder the terms for easier multiplication: 23x + -5 * 2x * x + 3 = 0 Multiply -5 * 2 23x + -10x * x + 3 = 0 Multiply x * x 23x + -10x2 + 3 = 0 Reorder the terms: 3 + 23x + -10x2 = 0 Solving 3 + 23x + -10x2 = 0 Solving for variable 'x'. 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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