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Simplifying x2 + -0.7x + -15 = -0.3 Reorder the terms: -15 + -0.7x + x2 = -0.3 Solving -15 + -0.7x + x2 = -0.3 Solving for variable 'x'. Reorder the terms: -15 + 0.3 + -0.7x + x2 = -0.3 + 0.3 Combine like terms: -15 + 0.3 = -14.7 -14.7 + -0.7x + x2 = -0.3 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 -14.7 + -0.7x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '14.7' to each side of the equation. -14.7 + -0.7x + 14.7 + x2 = 0.0 + 14.7 Reorder the terms: -14.7 + 14.7 + -0.7x + x2 = 0.0 + 14.7 Combine like terms: -14.7 + 14.7 = 0.0 0.0 + -0.7x + x2 = 0.0 + 14.7 -0.7x + x2 = 0.0 + 14.7 Combine like terms: 0.0 + 14.7 = 14.7 -0.7x + x2 = 14.7 The x term is -0.7x. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7x + 0.1225 + x2 = 14.7 + 0.1225 Reorder the terms: 0.1225 + -0.7x + x2 = 14.7 + 0.1225 Combine like terms: 14.7 + 0.1225 = 14.8225 0.1225 + -0.7x + x2 = 14.8225 Factor a perfect square on the left side: (x + -0.35)(x + -0.35) = 14.8225 Calculate the square root of the right side: 3.85 Break this problem into two subproblems by setting (x + -0.35) equal to 3.85 and -3.85.Subproblem 1
x + -0.35 = 3.85 Simplifying x + -0.35 = 3.85 Reorder the terms: -0.35 + x = 3.85 Solving -0.35 + x = 3.85 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = 3.85 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = 3.85 + 0.35 x = 3.85 + 0.35 Combine like terms: 3.85 + 0.35 = 4.2 x = 4.2 Simplifying x = 4.2Subproblem 2
x + -0.35 = -3.85 Simplifying x + -0.35 = -3.85 Reorder the terms: -0.35 + x = -3.85 Solving -0.35 + x = -3.85 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = -3.85 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = -3.85 + 0.35 x = -3.85 + 0.35 Combine like terms: -3.85 + 0.35 = -3.5 x = -3.5 Simplifying x = -3.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.2, -3.5}
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