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Simplifying 162512902010535673x2 + 367486861032556x + -146948092170028229 = 0 Reorder the terms: -146948092170028229 + 367486861032556x + 162512902010535673x2 = 0 Solving -146948092170028229 + 367486861032556x + 162512902010535673x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 162512902010535673 the coefficient of the squared term: Divide each side by '162512902010535673'. -0.9042241591 + 0.002261278068x + x2 = 0 Move the constant term to the right: Add '0.9042241591' to each side of the equation. -0.9042241591 + 0.002261278068x + 0.9042241591 + x2 = 0 + 0.9042241591 Reorder the terms: -0.9042241591 + 0.9042241591 + 0.002261278068x + x2 = 0 + 0.9042241591 Combine like terms: -0.9042241591 + 0.9042241591 = 0.0000000000 0.0000000000 + 0.002261278068x + x2 = 0 + 0.9042241591 0.002261278068x + x2 = 0 + 0.9042241591 Combine like terms: 0 + 0.9042241591 = 0.9042241591 0.002261278068x + x2 = 0.9042241591 The x term is 0.002261278068x. Take half its coefficient (0.001130639034). Square it (0.000001278344625) and add it to both sides. Add '0.000001278344625' to each side of the equation. 0.002261278068x + 0.000001278344625 + x2 = 0.9042241591 + 0.000001278344625 Reorder the terms: 0.000001278344625 + 0.002261278068x + x2 = 0.9042241591 + 0.000001278344625 Combine like terms: 0.9042241591 + 0.000001278344625 = 0.904225437444625 0.000001278344625 + 0.002261278068x + x2 = 0.904225437444625 Factor a perfect square on the left side: (x + 0.001130639034)(x + 0.001130639034) = 0.904225437444625 Calculate the square root of the right side: 0.950907691 Break this problem into two subproblems by setting (x + 0.001130639034) equal to 0.950907691 and -0.950907691.Subproblem 1
x + 0.001130639034 = 0.950907691 Simplifying x + 0.001130639034 = 0.950907691 Reorder the terms: 0.001130639034 + x = 0.950907691 Solving 0.001130639034 + x = 0.950907691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.001130639034' to each side of the equation. 0.001130639034 + -0.001130639034 + x = 0.950907691 + -0.001130639034 Combine like terms: 0.001130639034 + -0.001130639034 = 0.000000000000 0.000000000000 + x = 0.950907691 + -0.001130639034 x = 0.950907691 + -0.001130639034 Combine like terms: 0.950907691 + -0.001130639034 = 0.949777051966 x = 0.949777051966 Simplifying x = 0.949777051966Subproblem 2
x + 0.001130639034 = -0.950907691 Simplifying x + 0.001130639034 = -0.950907691 Reorder the terms: 0.001130639034 + x = -0.950907691 Solving 0.001130639034 + x = -0.950907691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.001130639034' to each side of the equation. 0.001130639034 + -0.001130639034 + x = -0.950907691 + -0.001130639034 Combine like terms: 0.001130639034 + -0.001130639034 = 0.000000000000 0.000000000000 + x = -0.950907691 + -0.001130639034 x = -0.950907691 + -0.001130639034 Combine like terms: -0.950907691 + -0.001130639034 = -0.952038330034 x = -0.952038330034 Simplifying x = -0.952038330034Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.949777051966, -0.952038330034}
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