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Simplifying -4.9x2 + 13.8x + 2 = 4 Reorder the terms: 2 + 13.8x + -4.9x2 = 4 Solving 2 + 13.8x + -4.9x2 = 4 Solving for variable 'x'. Reorder the terms: 2 + -4 + 13.8x + -4.9x2 = 4 + -4 Combine like terms: 2 + -4 = -2 -2 + 13.8x + -4.9x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -2 + 13.8x + -4.9x2 = 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 + -2.816326531x + x2 = 0 Move the constant term to the right: Add '-0.4081632653' to each side of the equation. 0.4081632653 + -2.816326531x + -0.4081632653 + x2 = 0 + -0.4081632653 Reorder the terms: 0.4081632653 + -0.4081632653 + -2.816326531x + x2 = 0 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + -2.816326531x + x2 = 0 + -0.4081632653 -2.816326531x + x2 = 0 + -0.4081632653 Combine like terms: 0 + -0.4081632653 = -0.4081632653 -2.816326531x + x2 = -0.4081632653 The x term is -2.816326531x. Take half its coefficient (-1.408163266). Square it (1.982923784) and add it to both sides. Add '1.982923784' to each side of the equation. -2.816326531x + 1.982923784 + x2 = -0.4081632653 + 1.982923784 Reorder the terms: 1.982923784 + -2.816326531x + x2 = -0.4081632653 + 1.982923784 Combine like terms: -0.4081632653 + 1.982923784 = 1.5747605187 1.982923784 + -2.816326531x + x2 = 1.5747605187 Factor a perfect square on the left side: (x + -1.408163266)(x + -1.408163266) = 1.5747605187 Calculate the square root of the right side: 1.254894625 Break this problem into two subproblems by setting (x + -1.408163266) equal to 1.254894625 and -1.254894625.Subproblem 1
x + -1.408163266 = 1.254894625 Simplifying x + -1.408163266 = 1.254894625 Reorder the terms: -1.408163266 + x = 1.254894625 Solving -1.408163266 + x = 1.254894625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.408163266' to each side of the equation. -1.408163266 + 1.408163266 + x = 1.254894625 + 1.408163266 Combine like terms: -1.408163266 + 1.408163266 = 0.000000000 0.000000000 + x = 1.254894625 + 1.408163266 x = 1.254894625 + 1.408163266 Combine like terms: 1.254894625 + 1.408163266 = 2.663057891 x = 2.663057891 Simplifying x = 2.663057891Subproblem 2
x + -1.408163266 = -1.254894625 Simplifying x + -1.408163266 = -1.254894625 Reorder the terms: -1.408163266 + x = -1.254894625 Solving -1.408163266 + x = -1.254894625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.408163266' to each side of the equation. -1.408163266 + 1.408163266 + x = -1.254894625 + 1.408163266 Combine like terms: -1.408163266 + 1.408163266 = 0.000000000 0.000000000 + x = -1.254894625 + 1.408163266 x = -1.254894625 + 1.408163266 Combine like terms: -1.254894625 + 1.408163266 = 0.153268641 x = 0.153268641 Simplifying x = 0.153268641Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.663057891, 0.153268641}
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