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Simplifying 8.48(0.12 + -0.70x + x2) = x (0.12 * 8.48 + -0.70x * 8.48 + x2 * 8.48) = x (1.0176 + -5.936x + 8.48x2) = x Solving 1.0176 + -5.936x + 8.48x2 = x Solving for variable 'x'. Reorder the terms: 1.0176 + -5.936x + -1x + 8.48x2 = x + -1x Combine like terms: -5.936x + -1x = -6.936x 1.0176 + -6.936x + 8.48x2 = x + -1x Combine like terms: x + -1x = 0 1.0176 + -6.936x + 8.48x2 = 0 Begin completing the square. Divide all terms by 8.48 the coefficient of the squared term: Divide each side by '8.48'. 0.12 + -0.8179245283x + x2 = 0 Move the constant term to the right: Add '-0.12' to each side of the equation. 0.12 + -0.8179245283x + -0.12 + x2 = 0 + -0.12 Reorder the terms: 0.12 + -0.12 + -0.8179245283x + x2 = 0 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + -0.8179245283x + x2 = 0 + -0.12 -0.8179245283x + x2 = 0 + -0.12 Combine like terms: 0 + -0.12 = -0.12 -0.8179245283x + x2 = -0.12 The x term is -0.8179245283x. Take half its coefficient (-0.4089622642). Square it (0.1672501335) and add it to both sides. Add '0.1672501335' to each side of the equation. -0.8179245283x + 0.1672501335 + x2 = -0.12 + 0.1672501335 Reorder the terms: 0.1672501335 + -0.8179245283x + x2 = -0.12 + 0.1672501335 Combine like terms: -0.12 + 0.1672501335 = 0.0472501335 0.1672501335 + -0.8179245283x + x2 = 0.0472501335 Factor a perfect square on the left side: (x + -0.4089622642)(x + -0.4089622642) = 0.0472501335 Calculate the square root of the right side: 0.217370958 Break this problem into two subproblems by setting (x + -0.4089622642) equal to 0.217370958 and -0.217370958.Subproblem 1
x + -0.4089622642 = 0.217370958 Simplifying x + -0.4089622642 = 0.217370958 Reorder the terms: -0.4089622642 + x = 0.217370958 Solving -0.4089622642 + x = 0.217370958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4089622642' to each side of the equation. -0.4089622642 + 0.4089622642 + x = 0.217370958 + 0.4089622642 Combine like terms: -0.4089622642 + 0.4089622642 = 0.0000000000 0.0000000000 + x = 0.217370958 + 0.4089622642 x = 0.217370958 + 0.4089622642 Combine like terms: 0.217370958 + 0.4089622642 = 0.6263332222 x = 0.6263332222 Simplifying x = 0.6263332222Subproblem 2
x + -0.4089622642 = -0.217370958 Simplifying x + -0.4089622642 = -0.217370958 Reorder the terms: -0.4089622642 + x = -0.217370958 Solving -0.4089622642 + x = -0.217370958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4089622642' to each side of the equation. -0.4089622642 + 0.4089622642 + x = -0.217370958 + 0.4089622642 Combine like terms: -0.4089622642 + 0.4089622642 = 0.0000000000 0.0000000000 + x = -0.217370958 + 0.4089622642 x = -0.217370958 + 0.4089622642 Combine like terms: -0.217370958 + 0.4089622642 = 0.1915913062 x = 0.1915913062 Simplifying x = 0.1915913062Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6263332222, 0.1915913062}
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