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Simplifying 75x2 + -90x + -4 = 0 Reorder the terms: -4 + -90x + 75x2 = 0 Solving -4 + -90x + 75x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 75 the coefficient of the squared term: Divide each side by '75'. -0.05333333333 + -1.2x + x2 = 0 Move the constant term to the right: Add '0.05333333333' to each side of the equation. -0.05333333333 + -1.2x + 0.05333333333 + x2 = 0 + 0.05333333333 Reorder the terms: -0.05333333333 + 0.05333333333 + -1.2x + x2 = 0 + 0.05333333333 Combine like terms: -0.05333333333 + 0.05333333333 = 0.00000000000 0.00000000000 + -1.2x + x2 = 0 + 0.05333333333 -1.2x + x2 = 0 + 0.05333333333 Combine like terms: 0 + 0.05333333333 = 0.05333333333 -1.2x + x2 = 0.05333333333 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 0.05333333333 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 0.05333333333 + 0.36 Combine like terms: 0.05333333333 + 0.36 = 0.41333333333 0.36 + -1.2x + x2 = 0.41333333333 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 0.41333333333 Calculate the square root of the right side: 0.642910051 Break this problem into two subproblems by setting (x + -0.6) equal to 0.642910051 and -0.642910051.Subproblem 1
x + -0.6 = 0.642910051 Simplifying x + -0.6 = 0.642910051 Reorder the terms: -0.6 + x = 0.642910051 Solving -0.6 + x = 0.642910051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.642910051 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.642910051 + 0.6 x = 0.642910051 + 0.6 Combine like terms: 0.642910051 + 0.6 = 1.242910051 x = 1.242910051 Simplifying x = 1.242910051Subproblem 2
x + -0.6 = -0.642910051 Simplifying x + -0.6 = -0.642910051 Reorder the terms: -0.6 + x = -0.642910051 Solving -0.6 + x = -0.642910051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -0.642910051 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.642910051 + 0.6 x = -0.642910051 + 0.6 Combine like terms: -0.642910051 + 0.6 = -0.042910051 x = -0.042910051 Simplifying x = -0.042910051Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.242910051, -0.042910051}
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