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Simplifying 7x2 + 4x + -17 = 55 + -15x Reorder the terms: -17 + 4x + 7x2 = 55 + -15x Solving -17 + 4x + 7x2 = 55 + -15x Solving for variable 'x'. Reorder the terms: -17 + -55 + 4x + 15x + 7x2 = 55 + -15x + -55 + 15x Combine like terms: -17 + -55 = -72 -72 + 4x + 15x + 7x2 = 55 + -15x + -55 + 15x Combine like terms: 4x + 15x = 19x -72 + 19x + 7x2 = 55 + -15x + -55 + 15x Reorder the terms: -72 + 19x + 7x2 = 55 + -55 + -15x + 15x Combine like terms: 55 + -55 = 0 -72 + 19x + 7x2 = 0 + -15x + 15x -72 + 19x + 7x2 = -15x + 15x Combine like terms: -15x + 15x = 0 -72 + 19x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -10.28571429 + 2.714285714x + x2 = 0 Move the constant term to the right: Add '10.28571429' to each side of the equation. -10.28571429 + 2.714285714x + 10.28571429 + x2 = 0 + 10.28571429 Reorder the terms: -10.28571429 + 10.28571429 + 2.714285714x + x2 = 0 + 10.28571429 Combine like terms: -10.28571429 + 10.28571429 = 0.00000000 0.00000000 + 2.714285714x + x2 = 0 + 10.28571429 2.714285714x + x2 = 0 + 10.28571429 Combine like terms: 0 + 10.28571429 = 10.28571429 2.714285714x + x2 = 10.28571429 The x term is 2.714285714x. Take half its coefficient (1.357142857). Square it (1.841836734) and add it to both sides. Add '1.841836734' to each side of the equation. 2.714285714x + 1.841836734 + x2 = 10.28571429 + 1.841836734 Reorder the terms: 1.841836734 + 2.714285714x + x2 = 10.28571429 + 1.841836734 Combine like terms: 10.28571429 + 1.841836734 = 12.127551024 1.841836734 + 2.714285714x + x2 = 12.127551024 Factor a perfect square on the left side: (x + 1.357142857)(x + 1.357142857) = 12.127551024 Calculate the square root of the right side: 3.482463356 Break this problem into two subproblems by setting (x + 1.357142857) equal to 3.482463356 and -3.482463356.Subproblem 1
x + 1.357142857 = 3.482463356 Simplifying x + 1.357142857 = 3.482463356 Reorder the terms: 1.357142857 + x = 3.482463356 Solving 1.357142857 + x = 3.482463356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.357142857' to each side of the equation. 1.357142857 + -1.357142857 + x = 3.482463356 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = 3.482463356 + -1.357142857 x = 3.482463356 + -1.357142857 Combine like terms: 3.482463356 + -1.357142857 = 2.125320499 x = 2.125320499 Simplifying x = 2.125320499Subproblem 2
x + 1.357142857 = -3.482463356 Simplifying x + 1.357142857 = -3.482463356 Reorder the terms: 1.357142857 + x = -3.482463356 Solving 1.357142857 + x = -3.482463356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.357142857' to each side of the equation. 1.357142857 + -1.357142857 + x = -3.482463356 + -1.357142857 Combine like terms: 1.357142857 + -1.357142857 = 0.000000000 0.000000000 + x = -3.482463356 + -1.357142857 x = -3.482463356 + -1.357142857 Combine like terms: -3.482463356 + -1.357142857 = -4.839606213 x = -4.839606213 Simplifying x = -4.839606213Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.125320499, -4.839606213}
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