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Simplifying x2 + -7x = 13 Reorder the terms: -7x + x2 = 13 Solving -7x + x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + -7x + x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -7x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -7x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -7x + x2 = 0 + 13 -7x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -7x + x2 = 13 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 13 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 13 + 12.25 Combine like terms: 13 + 12.25 = 25.25 12.25 + -7x + x2 = 25.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (x + -3.5) equal to 5.024937811 and -5.024937811.Subproblem 1
x + -3.5 = 5.024937811 Simplifying x + -3.5 = 5.024937811 Reorder the terms: -3.5 + x = 5.024937811 Solving -3.5 + x = 5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 5.024937811 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 5.024937811 + 3.5 x = 5.024937811 + 3.5 Combine like terms: 5.024937811 + 3.5 = 8.524937811 x = 8.524937811 Simplifying x = 8.524937811Subproblem 2
x + -3.5 = -5.024937811 Simplifying x + -3.5 = -5.024937811 Reorder the terms: -3.5 + x = -5.024937811 Solving -3.5 + x = -5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -5.024937811 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -5.024937811 + 3.5 x = -5.024937811 + 3.5 Combine like terms: -5.024937811 + 3.5 = -1.524937811 x = -1.524937811 Simplifying x = -1.524937811Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.524937811, -1.524937811}
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