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Simplifying 4x2 + 9x + -130 = 0 Reorder the terms: -130 + 9x + 4x2 = 0 Solving -130 + 9x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -32.5 + 2.25x + x2 = 0 Move the constant term to the right: Add '32.5' to each side of the equation. -32.5 + 2.25x + 32.5 + x2 = 0 + 32.5 Reorder the terms: -32.5 + 32.5 + 2.25x + x2 = 0 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + 2.25x + x2 = 0 + 32.5 2.25x + x2 = 0 + 32.5 Combine like terms: 0 + 32.5 = 32.5 2.25x + x2 = 32.5 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 32.5 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 32.5 + 1.265625 Combine like terms: 32.5 + 1.265625 = 33.765625 1.265625 + 2.25x + x2 = 33.765625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 33.765625 Calculate the square root of the right side: 5.81081965 Break this problem into two subproblems by setting (x + 1.125) equal to 5.81081965 and -5.81081965.Subproblem 1
x + 1.125 = 5.81081965 Simplifying x + 1.125 = 5.81081965 Reorder the terms: 1.125 + x = 5.81081965 Solving 1.125 + x = 5.81081965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 5.81081965 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 5.81081965 + -1.125 x = 5.81081965 + -1.125 Combine like terms: 5.81081965 + -1.125 = 4.68581965 x = 4.68581965 Simplifying x = 4.68581965Subproblem 2
x + 1.125 = -5.81081965 Simplifying x + 1.125 = -5.81081965 Reorder the terms: 1.125 + x = -5.81081965 Solving 1.125 + x = -5.81081965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -5.81081965 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -5.81081965 + -1.125 x = -5.81081965 + -1.125 Combine like terms: -5.81081965 + -1.125 = -6.93581965 x = -6.93581965 Simplifying x = -6.93581965Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.68581965, -6.93581965}
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