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Simplifying 35x2 + -69x + 20 = 7x2 + -8 Reorder the terms: 20 + -69x + 35x2 = 7x2 + -8 Reorder the terms: 20 + -69x + 35x2 = -8 + 7x2 Solving 20 + -69x + 35x2 = -8 + 7x2 Solving for variable 'x'. Reorder the terms: 20 + 8 + -69x + 35x2 + -7x2 = -8 + 7x2 + 8 + -7x2 Combine like terms: 20 + 8 = 28 28 + -69x + 35x2 + -7x2 = -8 + 7x2 + 8 + -7x2 Combine like terms: 35x2 + -7x2 = 28x2 28 + -69x + 28x2 = -8 + 7x2 + 8 + -7x2 Reorder the terms: 28 + -69x + 28x2 = -8 + 8 + 7x2 + -7x2 Combine like terms: -8 + 8 = 0 28 + -69x + 28x2 = 0 + 7x2 + -7x2 28 + -69x + 28x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 28 + -69x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. 1 + -2.464285714x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.464285714x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -2.464285714x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.464285714x + x2 = 0 + -1 -2.464285714x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.464285714x + x2 = -1 The x term is -2.464285714x. Take half its coefficient (-1.232142857). Square it (1.518176020) and add it to both sides. Add '1.518176020' to each side of the equation. -2.464285714x + 1.518176020 + x2 = -1 + 1.518176020 Reorder the terms: 1.518176020 + -2.464285714x + x2 = -1 + 1.518176020 Combine like terms: -1 + 1.518176020 = 0.51817602 1.518176020 + -2.464285714x + x2 = 0.51817602 Factor a perfect square on the left side: (x + -1.232142857)(x + -1.232142857) = 0.51817602 Calculate the square root of the right side: 0.719844442 Break this problem into two subproblems by setting (x + -1.232142857) equal to 0.719844442 and -0.719844442.Subproblem 1
x + -1.232142857 = 0.719844442 Simplifying x + -1.232142857 = 0.719844442 Reorder the terms: -1.232142857 + x = 0.719844442 Solving -1.232142857 + x = 0.719844442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.232142857' to each side of the equation. -1.232142857 + 1.232142857 + x = 0.719844442 + 1.232142857 Combine like terms: -1.232142857 + 1.232142857 = 0.000000000 0.000000000 + x = 0.719844442 + 1.232142857 x = 0.719844442 + 1.232142857 Combine like terms: 0.719844442 + 1.232142857 = 1.951987299 x = 1.951987299 Simplifying x = 1.951987299Subproblem 2
x + -1.232142857 = -0.719844442 Simplifying x + -1.232142857 = -0.719844442 Reorder the terms: -1.232142857 + x = -0.719844442 Solving -1.232142857 + x = -0.719844442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.232142857' to each side of the equation. -1.232142857 + 1.232142857 + x = -0.719844442 + 1.232142857 Combine like terms: -1.232142857 + 1.232142857 = 0.000000000 0.000000000 + x = -0.719844442 + 1.232142857 x = -0.719844442 + 1.232142857 Combine like terms: -0.719844442 + 1.232142857 = 0.512298415 x = 0.512298415 Simplifying x = 0.512298415Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.951987299, 0.512298415}
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