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Simplifying -16.1x2 + 4x + 10 = 0 Reorder the terms: 10 + 4x + -16.1x2 = 0 Solving 10 + 4x + -16.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16.1 the coefficient of the squared term: Divide each side by '-16.1'. -0.6211180124 + -0.248447205x + x2 = 0 Move the constant term to the right: Add '0.6211180124' to each side of the equation. -0.6211180124 + -0.248447205x + 0.6211180124 + x2 = 0 + 0.6211180124 Reorder the terms: -0.6211180124 + 0.6211180124 + -0.248447205x + x2 = 0 + 0.6211180124 Combine like terms: -0.6211180124 + 0.6211180124 = 0.0000000000 0.0000000000 + -0.248447205x + x2 = 0 + 0.6211180124 -0.248447205x + x2 = 0 + 0.6211180124 Combine like terms: 0 + 0.6211180124 = 0.6211180124 -0.248447205x + x2 = 0.6211180124 The x term is -0.248447205x. Take half its coefficient (-0.1242236025). Square it (0.01543150342) and add it to both sides. Add '0.01543150342' to each side of the equation. -0.248447205x + 0.01543150342 + x2 = 0.6211180124 + 0.01543150342 Reorder the terms: 0.01543150342 + -0.248447205x + x2 = 0.6211180124 + 0.01543150342 Combine like terms: 0.6211180124 + 0.01543150342 = 0.63654951582 0.01543150342 + -0.248447205x + x2 = 0.63654951582 Factor a perfect square on the left side: (x + -0.1242236025)(x + -0.1242236025) = 0.63654951582 Calculate the square root of the right side: 0.797840533 Break this problem into two subproblems by setting (x + -0.1242236025) equal to 0.797840533 and -0.797840533.Subproblem 1
x + -0.1242236025 = 0.797840533 Simplifying x + -0.1242236025 = 0.797840533 Reorder the terms: -0.1242236025 + x = 0.797840533 Solving -0.1242236025 + x = 0.797840533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1242236025' to each side of the equation. -0.1242236025 + 0.1242236025 + x = 0.797840533 + 0.1242236025 Combine like terms: -0.1242236025 + 0.1242236025 = 0.0000000000 0.0000000000 + x = 0.797840533 + 0.1242236025 x = 0.797840533 + 0.1242236025 Combine like terms: 0.797840533 + 0.1242236025 = 0.9220641355 x = 0.9220641355 Simplifying x = 0.9220641355Subproblem 2
x + -0.1242236025 = -0.797840533 Simplifying x + -0.1242236025 = -0.797840533 Reorder the terms: -0.1242236025 + x = -0.797840533 Solving -0.1242236025 + x = -0.797840533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1242236025' to each side of the equation. -0.1242236025 + 0.1242236025 + x = -0.797840533 + 0.1242236025 Combine like terms: -0.1242236025 + 0.1242236025 = 0.0000000000 0.0000000000 + x = -0.797840533 + 0.1242236025 x = -0.797840533 + 0.1242236025 Combine like terms: -0.797840533 + 0.1242236025 = -0.6736169305 x = -0.6736169305 Simplifying x = -0.6736169305Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9220641355, -0.6736169305}
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