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Simplifying 5x2 + -10x + -47 = -3 Reorder the terms: -47 + -10x + 5x2 = -3 Solving -47 + -10x + 5x2 = -3 Solving for variable 'x'. Reorder the terms: -47 + 3 + -10x + 5x2 = -3 + 3 Combine like terms: -47 + 3 = -44 -44 + -10x + 5x2 = -3 + 3 Combine like terms: -3 + 3 = 0 -44 + -10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -8.8 + -2x + x2 = 0 Move the constant term to the right: Add '8.8' to each side of the equation. -8.8 + -2x + 8.8 + x2 = 0 + 8.8 Reorder the terms: -8.8 + 8.8 + -2x + x2 = 0 + 8.8 Combine like terms: -8.8 + 8.8 = 0.0 0.0 + -2x + x2 = 0 + 8.8 -2x + x2 = 0 + 8.8 Combine like terms: 0 + 8.8 = 8.8 -2x + x2 = 8.8 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 = 8.8 + 1 Reorder the terms: 1 + -2x + x2 = 8.8 + 1 Combine like terms: 8.8 + 1 = 9.8 1 + -2x + x2 = 9.8 Factor a perfect square on the left side: (x + -1)(x + -1) = 9.8 Calculate the square root of the right side: 3.130495169 Break this problem into two subproblems by setting (x + -1) equal to 3.130495169 and -3.130495169.Subproblem 1
x + -1 = 3.130495169 Simplifying x + -1 = 3.130495169 Reorder the terms: -1 + x = 3.130495169 Solving -1 + x = 3.130495169 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 = 3.130495169 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.130495169 + 1 x = 3.130495169 + 1 Combine like terms: 3.130495169 + 1 = 4.130495169 x = 4.130495169 Simplifying x = 4.130495169Subproblem 2
x + -1 = -3.130495169 Simplifying x + -1 = -3.130495169 Reorder the terms: -1 + x = -3.130495169 Solving -1 + x = -3.130495169 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 = -3.130495169 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.130495169 + 1 x = -3.130495169 + 1 Combine like terms: -3.130495169 + 1 = -2.130495169 x = -2.130495169 Simplifying x = -2.130495169Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.130495169, -2.130495169}
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