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Simplifying 7x2 + 11x = 10 Reorder the terms: 11x + 7x2 = 10 Solving 11x + 7x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 11x + 7x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 11x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.428571429 + 1.571428571x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + 1.571428571x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + 1.571428571x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + 1.571428571x + x2 = 0 + 1.428571429 1.571428571x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 1.571428571x + x2 = 1.428571429 The x term is 1.571428571x. Take half its coefficient (0.7857142855). Square it (0.6173469384) and add it to both sides. Add '0.6173469384' to each side of the equation. 1.571428571x + 0.6173469384 + x2 = 1.428571429 + 0.6173469384 Reorder the terms: 0.6173469384 + 1.571428571x + x2 = 1.428571429 + 0.6173469384 Combine like terms: 1.428571429 + 0.6173469384 = 2.0459183674 0.6173469384 + 1.571428571x + x2 = 2.0459183674 Factor a perfect square on the left side: (x + 0.7857142855)(x + 0.7857142855) = 2.0459183674 Calculate the square root of the right side: 1.430356028 Break this problem into two subproblems by setting (x + 0.7857142855) equal to 1.430356028 and -1.430356028.Subproblem 1
x + 0.7857142855 = 1.430356028 Simplifying x + 0.7857142855 = 1.430356028 Reorder the terms: 0.7857142855 + x = 1.430356028 Solving 0.7857142855 + x = 1.430356028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x = 1.430356028 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = 1.430356028 + -0.7857142855 x = 1.430356028 + -0.7857142855 Combine like terms: 1.430356028 + -0.7857142855 = 0.6446417425 x = 0.6446417425 Simplifying x = 0.6446417425Subproblem 2
x + 0.7857142855 = -1.430356028 Simplifying x + 0.7857142855 = -1.430356028 Reorder the terms: 0.7857142855 + x = -1.430356028 Solving 0.7857142855 + x = -1.430356028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x = -1.430356028 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = -1.430356028 + -0.7857142855 x = -1.430356028 + -0.7857142855 Combine like terms: -1.430356028 + -0.7857142855 = -2.2160703135 x = -2.2160703135 Simplifying x = -2.2160703135Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6446417425, -2.2160703135}
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