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Simplifying x2 + 5.04x + -0.99792 = 0 Reorder the terms: -0.99792 + 5.04x + x2 = 0 Solving -0.99792 + 5.04x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.99792' to each side of the equation. -0.99792 + 5.04x + 0.99792 + x2 = 0 + 0.99792 Reorder the terms: -0.99792 + 0.99792 + 5.04x + x2 = 0 + 0.99792 Combine like terms: -0.99792 + 0.99792 = 0.00000 0.00000 + 5.04x + x2 = 0 + 0.99792 5.04x + x2 = 0 + 0.99792 Combine like terms: 0 + 0.99792 = 0.99792 5.04x + x2 = 0.99792 The x term is 5.04x. Take half its coefficient (2.52). Square it (6.3504) and add it to both sides. Add '6.3504' to each side of the equation. 5.04x + 6.3504 + x2 = 0.99792 + 6.3504 Reorder the terms: 6.3504 + 5.04x + x2 = 0.99792 + 6.3504 Combine like terms: 0.99792 + 6.3504 = 7.34832 6.3504 + 5.04x + x2 = 7.34832 Factor a perfect square on the left side: (x + 2.52)(x + 2.52) = 7.34832 Calculate the square root of the right side: 2.710778486 Break this problem into two subproblems by setting (x + 2.52) equal to 2.710778486 and -2.710778486.Subproblem 1
x + 2.52 = 2.710778486 Simplifying x + 2.52 = 2.710778486 Reorder the terms: 2.52 + x = 2.710778486 Solving 2.52 + x = 2.710778486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.52' to each side of the equation. 2.52 + -2.52 + x = 2.710778486 + -2.52 Combine like terms: 2.52 + -2.52 = 0.00 0.00 + x = 2.710778486 + -2.52 x = 2.710778486 + -2.52 Combine like terms: 2.710778486 + -2.52 = 0.190778486 x = 0.190778486 Simplifying x = 0.190778486Subproblem 2
x + 2.52 = -2.710778486 Simplifying x + 2.52 = -2.710778486 Reorder the terms: 2.52 + x = -2.710778486 Solving 2.52 + x = -2.710778486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.52' to each side of the equation. 2.52 + -2.52 + x = -2.710778486 + -2.52 Combine like terms: 2.52 + -2.52 = 0.00 0.00 + x = -2.710778486 + -2.52 x = -2.710778486 + -2.52 Combine like terms: -2.710778486 + -2.52 = -5.230778486 x = -5.230778486 Simplifying x = -5.230778486Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.190778486, -5.230778486}
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