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Simplifying x2 = 5x + 19 Reorder the terms: x2 = 19 + 5x Solving x2 = 19 + 5x Solving for variable 'x'. Reorder the terms: -19 + -5x + x2 = 19 + 5x + -19 + -5x Reorder the terms: -19 + -5x + x2 = 19 + -19 + 5x + -5x Combine like terms: 19 + -19 = 0 -19 + -5x + x2 = 0 + 5x + -5x -19 + -5x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -19 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -5x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -5x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -5x + x2 = 0 + 19 -5x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -5x + x2 = 19 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 19 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 19 + 6.25 Combine like terms: 19 + 6.25 = 25.25 6.25 + -5x + x2 = 25.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (x + -2.5) equal to 5.024937811 and -5.024937811.Subproblem 1
x + -2.5 = 5.024937811 Simplifying x + -2.5 = 5.024937811 Reorder the terms: -2.5 + x = 5.024937811 Solving -2.5 + x = 5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 5.024937811 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 5.024937811 + 2.5 x = 5.024937811 + 2.5 Combine like terms: 5.024937811 + 2.5 = 7.524937811 x = 7.524937811 Simplifying x = 7.524937811Subproblem 2
x + -2.5 = -5.024937811 Simplifying x + -2.5 = -5.024937811 Reorder the terms: -2.5 + x = -5.024937811 Solving -2.5 + x = -5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -5.024937811 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -5.024937811 + 2.5 x = -5.024937811 + 2.5 Combine like terms: -5.024937811 + 2.5 = -2.524937811 x = -2.524937811 Simplifying x = -2.524937811Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.524937811, -2.524937811}
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