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Simplifying 7.5x2 + -3x + -10.5 = 0 Reorder the terms: -10.5 + -3x + 7.5x2 = 0 Solving -10.5 + -3x + 7.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7.5 the coefficient of the squared term: Divide each side by '7.5'. -1.4 + -0.4x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -0.4x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -0.4x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -0.4x + x2 = 0 + 1.4 -0.4x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -0.4x + x2 = 1.4 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 1.4 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 1.4 + 0.04 Combine like terms: 1.4 + 0.04 = 1.44 0.04 + -0.4x + x2 = 1.44 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 1.44 Calculate the square root of the right side: 1.2 Break this problem into two subproblems by setting (x + -0.2) equal to 1.2 and -1.2.Subproblem 1
x + -0.2 = 1.2 Simplifying x + -0.2 = 1.2 Reorder the terms: -0.2 + x = 1.2 Solving -0.2 + x = 1.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 1.2 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 1.2 + 0.2 x = 1.2 + 0.2 Combine like terms: 1.2 + 0.2 = 1.4 x = 1.4 Simplifying x = 1.4Subproblem 2
x + -0.2 = -1.2 Simplifying x + -0.2 = -1.2 Reorder the terms: -0.2 + x = -1.2 Solving -0.2 + x = -1.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -1.2 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -1.2 + 0.2 x = -1.2 + 0.2 Combine like terms: -1.2 + 0.2 = -1 x = -1 Simplifying x = -1Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4, -1}
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