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Simplifying 42x2 + -69x + 28 = 0 Reorder the terms: 28 + -69x + 42x2 = 0 Solving 28 + -69x + 42x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. 0.6666666667 + -1.642857143x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -1.642857143x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -1.642857143x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -1.642857143x + x2 = 0 + -0.6666666667 -1.642857143x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -1.642857143x + x2 = -0.6666666667 The x term is -1.642857143x. Take half its coefficient (-0.8214285715). Square it (0.6747448981) and add it to both sides. Add '0.6747448981' to each side of the equation. -1.642857143x + 0.6747448981 + x2 = -0.6666666667 + 0.6747448981 Reorder the terms: 0.6747448981 + -1.642857143x + x2 = -0.6666666667 + 0.6747448981 Combine like terms: -0.6666666667 + 0.6747448981 = 0.0080782314 0.6747448981 + -1.642857143x + x2 = 0.0080782314 Factor a perfect square on the left side: (x + -0.8214285715)(x + -0.8214285715) = 0.0080782314 Calculate the square root of the right side: 0.089878982 Break this problem into two subproblems by setting (x + -0.8214285715) equal to 0.089878982 and -0.089878982.Subproblem 1
x + -0.8214285715 = 0.089878982 Simplifying x + -0.8214285715 = 0.089878982 Reorder the terms: -0.8214285715 + x = 0.089878982 Solving -0.8214285715 + x = 0.089878982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8214285715' to each side of the equation. -0.8214285715 + 0.8214285715 + x = 0.089878982 + 0.8214285715 Combine like terms: -0.8214285715 + 0.8214285715 = 0.0000000000 0.0000000000 + x = 0.089878982 + 0.8214285715 x = 0.089878982 + 0.8214285715 Combine like terms: 0.089878982 + 0.8214285715 = 0.9113075535 x = 0.9113075535 Simplifying x = 0.9113075535Subproblem 2
x + -0.8214285715 = -0.089878982 Simplifying x + -0.8214285715 = -0.089878982 Reorder the terms: -0.8214285715 + x = -0.089878982 Solving -0.8214285715 + x = -0.089878982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8214285715' to each side of the equation. -0.8214285715 + 0.8214285715 + x = -0.089878982 + 0.8214285715 Combine like terms: -0.8214285715 + 0.8214285715 = 0.0000000000 0.0000000000 + x = -0.089878982 + 0.8214285715 x = -0.089878982 + 0.8214285715 Combine like terms: -0.089878982 + 0.8214285715 = 0.7315495895 x = 0.7315495895 Simplifying x = 0.7315495895Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9113075535, 0.7315495895}
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