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Simplifying 52.3x2 + -74.62x + 26.117 = 0 Reorder the terms: 26.117 + -74.62x + 52.3x2 = 0 Solving 26.117 + -74.62x + 52.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 52.3 the coefficient of the squared term: Divide each side by '52.3'. 0.4993690249 + -1.426768642x + x2 = 0 Move the constant term to the right: Add '-0.4993690249' to each side of the equation. 0.4993690249 + -1.426768642x + -0.4993690249 + x2 = 0 + -0.4993690249 Reorder the terms: 0.4993690249 + -0.4993690249 + -1.426768642x + x2 = 0 + -0.4993690249 Combine like terms: 0.4993690249 + -0.4993690249 = 0.0000000000 0.0000000000 + -1.426768642x + x2 = 0 + -0.4993690249 -1.426768642x + x2 = 0 + -0.4993690249 Combine like terms: 0 + -0.4993690249 = -0.4993690249 -1.426768642x + x2 = -0.4993690249 The x term is -1.426768642x. Take half its coefficient (-0.713384321). Square it (0.5089171894) and add it to both sides. Add '0.5089171894' to each side of the equation. -1.426768642x + 0.5089171894 + x2 = -0.4993690249 + 0.5089171894 Reorder the terms: 0.5089171894 + -1.426768642x + x2 = -0.4993690249 + 0.5089171894 Combine like terms: -0.4993690249 + 0.5089171894 = 0.0095481645 0.5089171894 + -1.426768642x + x2 = 0.0095481645 Factor a perfect square on the left side: (x + -0.713384321)(x + -0.713384321) = 0.0095481645 Calculate the square root of the right side: 0.09771471 Break this problem into two subproblems by setting (x + -0.713384321) equal to 0.09771471 and -0.09771471.Subproblem 1
x + -0.713384321 = 0.09771471 Simplifying x + -0.713384321 = 0.09771471 Reorder the terms: -0.713384321 + x = 0.09771471 Solving -0.713384321 + x = 0.09771471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.713384321' to each side of the equation. -0.713384321 + 0.713384321 + x = 0.09771471 + 0.713384321 Combine like terms: -0.713384321 + 0.713384321 = 0.000000000 0.000000000 + x = 0.09771471 + 0.713384321 x = 0.09771471 + 0.713384321 Combine like terms: 0.09771471 + 0.713384321 = 0.811099031 x = 0.811099031 Simplifying x = 0.811099031Subproblem 2
x + -0.713384321 = -0.09771471 Simplifying x + -0.713384321 = -0.09771471 Reorder the terms: -0.713384321 + x = -0.09771471 Solving -0.713384321 + x = -0.09771471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.713384321' to each side of the equation. -0.713384321 + 0.713384321 + x = -0.09771471 + 0.713384321 Combine like terms: -0.713384321 + 0.713384321 = 0.000000000 0.000000000 + x = -0.09771471 + 0.713384321 x = -0.09771471 + 0.713384321 Combine like terms: -0.09771471 + 0.713384321 = 0.615669611 x = 0.615669611 Simplifying x = 0.615669611Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.811099031, 0.615669611}
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