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Simplifying 35x2 + -144x + 105 = 0 Reorder the terms: 105 + -144x + 35x2 = 0 Solving 105 + -144x + 35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. 3 + -4.114285714x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -4.114285714x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -4.114285714x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4.114285714x + x2 = 0 + -3 -4.114285714x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4.114285714x + x2 = -3 The x term is -4.114285714x. Take half its coefficient (-2.057142857). Square it (4.231836734) and add it to both sides. Add '4.231836734' to each side of the equation. -4.114285714x + 4.231836734 + x2 = -3 + 4.231836734 Reorder the terms: 4.231836734 + -4.114285714x + x2 = -3 + 4.231836734 Combine like terms: -3 + 4.231836734 = 1.231836734 4.231836734 + -4.114285714x + x2 = 1.231836734 Factor a perfect square on the left side: (x + -2.057142857)(x + -2.057142857) = 1.231836734 Calculate the square root of the right side: 1.109881405 Break this problem into two subproblems by setting (x + -2.057142857) equal to 1.109881405 and -1.109881405.Subproblem 1
x + -2.057142857 = 1.109881405 Simplifying x + -2.057142857 = 1.109881405 Reorder the terms: -2.057142857 + x = 1.109881405 Solving -2.057142857 + x = 1.109881405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.057142857' to each side of the equation. -2.057142857 + 2.057142857 + x = 1.109881405 + 2.057142857 Combine like terms: -2.057142857 + 2.057142857 = 0.000000000 0.000000000 + x = 1.109881405 + 2.057142857 x = 1.109881405 + 2.057142857 Combine like terms: 1.109881405 + 2.057142857 = 3.167024262 x = 3.167024262 Simplifying x = 3.167024262Subproblem 2
x + -2.057142857 = -1.109881405 Simplifying x + -2.057142857 = -1.109881405 Reorder the terms: -2.057142857 + x = -1.109881405 Solving -2.057142857 + x = -1.109881405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.057142857' to each side of the equation. -2.057142857 + 2.057142857 + x = -1.109881405 + 2.057142857 Combine like terms: -2.057142857 + 2.057142857 = 0.000000000 0.000000000 + x = -1.109881405 + 2.057142857 x = -1.109881405 + 2.057142857 Combine like terms: -1.109881405 + 2.057142857 = 0.947261452 x = 0.947261452 Simplifying x = 0.947261452Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.167024262, 0.947261452}
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