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Simplifying 5x2 + -10x = 7 Reorder the terms: -10x + 5x2 = 7 Solving -10x + 5x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -10x + 5x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -2x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -2x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -2x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -2x + x2 = 0 + 1.4 -2x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -2x + x2 = 1.4 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 = 1.4 + 1 Reorder the terms: 1 + -2x + x2 = 1.4 + 1 Combine like terms: 1.4 + 1 = 2.4 1 + -2x + x2 = 2.4 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.4 Calculate the square root of the right side: 1.549193338 Break this problem into two subproblems by setting (x + -1) equal to 1.549193338 and -1.549193338.Subproblem 1
x + -1 = 1.549193338 Simplifying x + -1 = 1.549193338 Reorder the terms: -1 + x = 1.549193338 Solving -1 + x = 1.549193338 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 = 1.549193338 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.549193338 + 1 x = 1.549193338 + 1 Combine like terms: 1.549193338 + 1 = 2.549193338 x = 2.549193338 Simplifying x = 2.549193338Subproblem 2
x + -1 = -1.549193338 Simplifying x + -1 = -1.549193338 Reorder the terms: -1 + x = -1.549193338 Solving -1 + x = -1.549193338 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 = -1.549193338 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.549193338 + 1 x = -1.549193338 + 1 Combine like terms: -1.549193338 + 1 = -0.549193338 x = -0.549193338 Simplifying x = -0.549193338Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.549193338, -0.549193338}
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