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Simplifying 0.1x2 + -4x + 0.7 = 0 Reorder the terms: 0.7 + -4x + 0.1x2 = 0 Solving 0.7 + -4x + 0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 7 + -40x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -40x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -40x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -40x + x2 = 0 + -7 -40x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -40x + x2 = -7 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -7 + 400 Reorder the terms: 400 + -40x + x2 = -7 + 400 Combine like terms: -7 + 400 = 393 400 + -40x + x2 = 393 Factor a perfect square on the left side: (x + -20)(x + -20) = 393 Calculate the square root of the right side: 19.824227602 Break this problem into two subproblems by setting (x + -20) equal to 19.824227602 and -19.824227602.Subproblem 1
x + -20 = 19.824227602 Simplifying x + -20 = 19.824227602 Reorder the terms: -20 + x = 19.824227602 Solving -20 + x = 19.824227602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 19.824227602 + 20 Combine like terms: -20 + 20 = 0 0 + x = 19.824227602 + 20 x = 19.824227602 + 20 Combine like terms: 19.824227602 + 20 = 39.824227602 x = 39.824227602 Simplifying x = 39.824227602Subproblem 2
x + -20 = -19.824227602 Simplifying x + -20 = -19.824227602 Reorder the terms: -20 + x = -19.824227602 Solving -20 + x = -19.824227602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -19.824227602 + 20 Combine like terms: -20 + 20 = 0 0 + x = -19.824227602 + 20 x = -19.824227602 + 20 Combine like terms: -19.824227602 + 20 = 0.175772398 x = 0.175772398 Simplifying x = 0.175772398Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.824227602, 0.175772398}
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