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Simplifying -4.9x2 + 3.5x + 10 = 1 Reorder the terms: 10 + 3.5x + -4.9x2 = 1 Solving 10 + 3.5x + -4.9x2 = 1 Solving for variable 'x'. Reorder the terms: 10 + -1 + 3.5x + -4.9x2 = 1 + -1 Combine like terms: 10 + -1 = 9 9 + 3.5x + -4.9x2 = 1 + -1 Combine like terms: 1 + -1 = 0 9 + 3.5x + -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'. -1.836734694 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '1.836734694' to each side of the equation. -1.836734694 + -0.7142857143x + 1.836734694 + x2 = 0 + 1.836734694 Reorder the terms: -1.836734694 + 1.836734694 + -0.7142857143x + x2 = 0 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + -0.7142857143x + x2 = 0 + 1.836734694 -0.7142857143x + x2 = 0 + 1.836734694 Combine like terms: 0 + 1.836734694 = 1.836734694 -0.7142857143x + x2 = 1.836734694 The x term is -0.7142857143x. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143x + 0.1275510204 + x2 = 1.836734694 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 1.836734694 + 0.1275510204 Combine like terms: 1.836734694 + 0.1275510204 = 1.9642857144 0.1275510204 + -0.7142857143x + x2 = 1.9642857144 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 1.9642857144 Calculate the square root of the right side: 1.401529776 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 1.401529776 and -1.401529776.Subproblem 1
x + -0.3571428572 = 1.401529776 Simplifying x + -0.3571428572 = 1.401529776 Reorder the terms: -0.3571428572 + x = 1.401529776 Solving -0.3571428572 + x = 1.401529776 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = 1.401529776 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 1.401529776 + 0.3571428572 x = 1.401529776 + 0.3571428572 Combine like terms: 1.401529776 + 0.3571428572 = 1.7586726332 x = 1.7586726332 Simplifying x = 1.7586726332Subproblem 2
x + -0.3571428572 = -1.401529776 Simplifying x + -0.3571428572 = -1.401529776 Reorder the terms: -0.3571428572 + x = -1.401529776 Solving -0.3571428572 + x = -1.401529776 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = -1.401529776 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -1.401529776 + 0.3571428572 x = -1.401529776 + 0.3571428572 Combine like terms: -1.401529776 + 0.3571428572 = -1.0443869188 x = -1.0443869188 Simplifying x = -1.0443869188Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7586726332, -1.0443869188}
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