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Simplifying 2x2 + 4x + -7 = 10 Reorder the terms: -7 + 4x + 2x2 = 10 Solving -7 + 4x + 2x2 = 10 Solving for variable 'x'. Reorder the terms: -7 + -10 + 4x + 2x2 = 10 + -10 Combine like terms: -7 + -10 = -17 -17 + 4x + 2x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -17 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8.5 + 2x + x2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + 2x + 8.5 + x2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + 2x + x2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + 2x + x2 = 0 + 8.5 2x + x2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 2x + x2 = 8.5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 8.5 + 1 Reorder the terms: 1 + 2x + x2 = 8.5 + 1 Combine like terms: 8.5 + 1 = 9.5 1 + 2x + x2 = 9.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (x + 1) equal to 3.082207001 and -3.082207001.Subproblem 1
x + 1 = 3.082207001 Simplifying x + 1 = 3.082207001 Reorder the terms: 1 + x = 3.082207001 Solving 1 + x = 3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.082207001 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.082207001 + -1 x = 3.082207001 + -1 Combine like terms: 3.082207001 + -1 = 2.082207001 x = 2.082207001 Simplifying x = 2.082207001Subproblem 2
x + 1 = -3.082207001 Simplifying x + 1 = -3.082207001 Reorder the terms: 1 + x = -3.082207001 Solving 1 + x = -3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.082207001 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.082207001 + -1 x = -3.082207001 + -1 Combine like terms: -3.082207001 + -1 = -4.082207001 x = -4.082207001 Simplifying x = -4.082207001Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.082207001, -4.082207001}
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