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Simplifying 70 = 7x2 + x + 4 + x + 4 Reorder the terms: 70 = 4 + 4 + x + x + 7x2 Combine like terms: 4 + 4 = 8 70 = 8 + x + x + 7x2 Combine like terms: x + x = 2x 70 = 8 + 2x + 7x2 Solving 70 = 8 + 2x + 7x2 Solving for variable 'x'. Combine like terms: 70 + -8 = 62 62 + -2x + -7x2 = 8 + 2x + 7x2 + -8 + -2x + -7x2 Reorder the terms: 62 + -2x + -7x2 = 8 + -8 + 2x + -2x + 7x2 + -7x2 Combine like terms: 8 + -8 = 0 62 + -2x + -7x2 = 0 + 2x + -2x + 7x2 + -7x2 62 + -2x + -7x2 = 2x + -2x + 7x2 + -7x2 Combine like terms: 2x + -2x = 0 62 + -2x + -7x2 = 0 + 7x2 + -7x2 62 + -2x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 62 + -2x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -8.857142857 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '8.857142857' to each side of the equation. -8.857142857 + 0.2857142857x + 8.857142857 + x2 = 0 + 8.857142857 Reorder the terms: -8.857142857 + 8.857142857 + 0.2857142857x + x2 = 0 + 8.857142857 Combine like terms: -8.857142857 + 8.857142857 = 0.000000000 0.000000000 + 0.2857142857x + x2 = 0 + 8.857142857 0.2857142857x + x2 = 0 + 8.857142857 Combine like terms: 0 + 8.857142857 = 8.857142857 0.2857142857x + x2 = 8.857142857 The x term is 0.2857142857x. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857x + 0.02040816328 + x2 = 8.857142857 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 8.857142857 + 0.02040816328 Combine like terms: 8.857142857 + 0.02040816328 = 8.87755102028 0.02040816328 + 0.2857142857x + x2 = 8.87755102028 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 8.87755102028 Calculate the square root of the right side: 2.979521945 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 2.979521945 and -2.979521945.Subproblem 1
x + 0.1428571429 = 2.979521945 Simplifying x + 0.1428571429 = 2.979521945 Reorder the terms: 0.1428571429 + x = 2.979521945 Solving 0.1428571429 + x = 2.979521945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = 2.979521945 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 2.979521945 + -0.1428571429 x = 2.979521945 + -0.1428571429 Combine like terms: 2.979521945 + -0.1428571429 = 2.8366648021 x = 2.8366648021 Simplifying x = 2.8366648021Subproblem 2
x + 0.1428571429 = -2.979521945 Simplifying x + 0.1428571429 = -2.979521945 Reorder the terms: 0.1428571429 + x = -2.979521945 Solving 0.1428571429 + x = -2.979521945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = -2.979521945 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -2.979521945 + -0.1428571429 x = -2.979521945 + -0.1428571429 Combine like terms: -2.979521945 + -0.1428571429 = -3.1223790879 x = -3.1223790879 Simplifying x = -3.1223790879Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.8366648021, -3.1223790879}
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