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Simplifying 0 = -4.9x2 + 14.79x + -2 Reorder the terms: 0 = -2 + 14.79x + -4.9x2 Solving 0 = -2 + 14.79x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + 2 = 2 2 + -14.79x + 4.9x2 = -2 + 14.79x + -4.9x2 + 2 + -14.79x + 4.9x2 Reorder the terms: 2 + -14.79x + 4.9x2 = -2 + 2 + 14.79x + -14.79x + -4.9x2 + 4.9x2 Combine like terms: -2 + 2 = 0 2 + -14.79x + 4.9x2 = 0 + 14.79x + -14.79x + -4.9x2 + 4.9x2 2 + -14.79x + 4.9x2 = 14.79x + -14.79x + -4.9x2 + 4.9x2 Combine like terms: 14.79x + -14.79x = 0.00 2 + -14.79x + 4.9x2 = 0.00 + -4.9x2 + 4.9x2 2 + -14.79x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 2 + -14.79x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 0.4081632653 + -3.018367347x + x2 = 0 Move the constant term to the right: Add '-0.4081632653' to each side of the equation. 0.4081632653 + -3.018367347x + -0.4081632653 + x2 = 0 + -0.4081632653 Reorder the terms: 0.4081632653 + -0.4081632653 + -3.018367347x + x2 = 0 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + -3.018367347x + x2 = 0 + -0.4081632653 -3.018367347x + x2 = 0 + -0.4081632653 Combine like terms: 0 + -0.4081632653 = -0.4081632653 -3.018367347x + x2 = -0.4081632653 The x term is -3.018367347x. Take half its coefficient (-1.509183674). Square it (2.277635362) and add it to both sides. Add '2.277635362' to each side of the equation. -3.018367347x + 2.277635362 + x2 = -0.4081632653 + 2.277635362 Reorder the terms: 2.277635362 + -3.018367347x + x2 = -0.4081632653 + 2.277635362 Combine like terms: -0.4081632653 + 2.277635362 = 1.8694720967 2.277635362 + -3.018367347x + x2 = 1.8694720967 Factor a perfect square on the left side: (x + -1.509183674)(x + -1.509183674) = 1.8694720967 Calculate the square root of the right side: 1.367286399 Break this problem into two subproblems by setting (x + -1.509183674) equal to 1.367286399 and -1.367286399.Subproblem 1
x + -1.509183674 = 1.367286399 Simplifying x + -1.509183674 = 1.367286399 Reorder the terms: -1.509183674 + x = 1.367286399 Solving -1.509183674 + x = 1.367286399 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.509183674' to each side of the equation. -1.509183674 + 1.509183674 + x = 1.367286399 + 1.509183674 Combine like terms: -1.509183674 + 1.509183674 = 0.000000000 0.000000000 + x = 1.367286399 + 1.509183674 x = 1.367286399 + 1.509183674 Combine like terms: 1.367286399 + 1.509183674 = 2.876470073 x = 2.876470073 Simplifying x = 2.876470073Subproblem 2
x + -1.509183674 = -1.367286399 Simplifying x + -1.509183674 = -1.367286399 Reorder the terms: -1.509183674 + x = -1.367286399 Solving -1.509183674 + x = -1.367286399 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.509183674' to each side of the equation. -1.509183674 + 1.509183674 + x = -1.367286399 + 1.509183674 Combine like terms: -1.509183674 + 1.509183674 = 0.000000000 0.000000000 + x = -1.367286399 + 1.509183674 x = -1.367286399 + 1.509183674 Combine like terms: -1.367286399 + 1.509183674 = 0.141897275 x = 0.141897275 Simplifying x = 0.141897275Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.876470073, 0.141897275}
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