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Simplifying x2 + 3x + -945 = 0 Reorder the terms: -945 + 3x + x2 = 0 Solving -945 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '945' to each side of the equation. -945 + 3x + 945 + x2 = 0 + 945 Reorder the terms: -945 + 945 + 3x + x2 = 0 + 945 Combine like terms: -945 + 945 = 0 0 + 3x + x2 = 0 + 945 3x + x2 = 0 + 945 Combine like terms: 0 + 945 = 945 3x + x2 = 945 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 945 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 945 + 2.25 Combine like terms: 945 + 2.25 = 947.25 2.25 + 3x + x2 = 947.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 947.25 Calculate the square root of the right side: 30.777426793 Break this problem into two subproblems by setting (x + 1.5) equal to 30.777426793 and -30.777426793.Subproblem 1
x + 1.5 = 30.777426793 Simplifying x + 1.5 = 30.777426793 Reorder the terms: 1.5 + x = 30.777426793 Solving 1.5 + x = 30.777426793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 30.777426793 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 30.777426793 + -1.5 x = 30.777426793 + -1.5 Combine like terms: 30.777426793 + -1.5 = 29.277426793 x = 29.277426793 Simplifying x = 29.277426793Subproblem 2
x + 1.5 = -30.777426793 Simplifying x + 1.5 = -30.777426793 Reorder the terms: 1.5 + x = -30.777426793 Solving 1.5 + x = -30.777426793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -30.777426793 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -30.777426793 + -1.5 x = -30.777426793 + -1.5 Combine like terms: -30.777426793 + -1.5 = -32.277426793 x = -32.277426793 Simplifying x = -32.277426793Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.277426793, -32.277426793}
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