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Simplifying 5x * 5x + -23x + -10 = 0 Reorder the terms for easier multiplication: 5 * 5x * x + -23x + -10 = 0 Multiply 5 * 5 25x * x + -23x + -10 = 0 Multiply x * x 25x2 + -23x + -10 = 0 Reorder the terms: -10 + -23x + 25x2 = 0 Solving -10 + -23x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.4 + -0.92x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -0.92x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -0.92x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -0.92x + x2 = 0 + 0.4 -0.92x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -0.92x + x2 = 0.4 The x term is -0.92x. Take half its coefficient (-0.46). Square it (0.2116) and add it to both sides. Add '0.2116' to each side of the equation. -0.92x + 0.2116 + x2 = 0.4 + 0.2116 Reorder the terms: 0.2116 + -0.92x + x2 = 0.4 + 0.2116 Combine like terms: 0.4 + 0.2116 = 0.6116 0.2116 + -0.92x + x2 = 0.6116 Factor a perfect square on the left side: (x + -0.46)(x + -0.46) = 0.6116 Calculate the square root of the right side: 0.782048592 Break this problem into two subproblems by setting (x + -0.46) equal to 0.782048592 and -0.782048592.Subproblem 1
x + -0.46 = 0.782048592 Simplifying x + -0.46 = 0.782048592 Reorder the terms: -0.46 + x = 0.782048592 Solving -0.46 + x = 0.782048592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.46' to each side of the equation. -0.46 + 0.46 + x = 0.782048592 + 0.46 Combine like terms: -0.46 + 0.46 = 0.00 0.00 + x = 0.782048592 + 0.46 x = 0.782048592 + 0.46 Combine like terms: 0.782048592 + 0.46 = 1.242048592 x = 1.242048592 Simplifying x = 1.242048592Subproblem 2
x + -0.46 = -0.782048592 Simplifying x + -0.46 = -0.782048592 Reorder the terms: -0.46 + x = -0.782048592 Solving -0.46 + x = -0.782048592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.46' to each side of the equation. -0.46 + 0.46 + x = -0.782048592 + 0.46 Combine like terms: -0.46 + 0.46 = 0.00 0.00 + x = -0.782048592 + 0.46 x = -0.782048592 + 0.46 Combine like terms: -0.782048592 + 0.46 = -0.322048592 x = -0.322048592 Simplifying x = -0.322048592Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.242048592, -0.322048592}
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